Bu zorluk, kare boyutunun, tahta boyunca sabit olmak yerine, aşağıda açıklandığı gibi, azalmayan belirli bir sırayı takip ettiği bir satranç tahtası inşa etmekle ilgilidir.

Kurul yinelemeli olarak tanımlanır. Büyüklükte bir kart $n \times n$ olacak şekilde genişletilir $(n+k)\times(n+k)$ boyutu karelerinden oluşan bir "tabaka" ile aşağı genişleterek ve sağa $k$ , $k$ büyük bölen bir $n$ değil aşan $\sqrt{n}$ . Diyagonaldeki kareler her zaman aynı renktedir.

Özellikle, olarak temsil renklerle kurulu düşünün #ve +.

1. Satranç tahtasını

   #
   

2. Kart şu ana kadar $1\times 1$ boyutuna sahip . Tek böleni $1$ olan $1$ ve aşmadığı $\sqrt{1}$ . Aldığımız Yani$k=1$ve boyutlarda kareler bir katman eklenerek kurulu uzatmak$1$ile#diyagonal içinde:

   #+
   +#
   

3. Şimdiye kadar inşa edilen tahta $2 \times 2$ boyutunda . Arasında bölenler $2$ olan $1,2$ , ve maksimum bölen aşmayan $\sqrt{2}$ ,$1$. Yani yine$k=1$ve tahta

   #+#
   +#+
   #+#
   

4. Boyut $3 \times 3$ . $k=1$ . Şuraya genişlet:

   #+#+
   +#+#
   #+#+
   +#+#
   

5. Boyut $4 \times 4$ . Şimdi $k=2$ , çünkü $2$ , $4$ geçmeyen maksimum bölücü $\sqrt 4$ . Diyagonalrenkte,2×2büyüklüğünde karelerden oluşan birkalınlık tabakası$2$ile genişletin:$2\times 2$#

   #+#+##
   +#+###
   #+#+++
   +#+#++
   ##++##
   ##++##
   

6. Boyut $6 \times 6$ . Şimdi $k=2$ . $8 \times 8$ boyutuna uzatın . Şimdi $k=2$ . $10 \times 10$ boyutuna uzatın . Şimdi $k=2$ . $12 \times 12$ boyutuna uzatın . Şimdi $k=3$ . $15$ bedene kadar genişlet :

   #+#+##++##++###
   +#+###++##++###
   #+#+++##++#####
   +#+#++##++##+++
   ##++##++##+++++
   ##++##++##+++++
   ++##++##++#####
   ++##++##++#####
   ##++##++##++###
   ##++##++##+++++
   ++##++##++##+++
   ++##++##++##+++
   ###+++###+++###
   ###+++###+++###
   ###+++###+++###
   

En son eklenen $3 \times 3$ boyutundaki karelerin, önceden eklenen $2 \times 2$ boyutundaki karelerle kısmen çakışan kenarlara sahip olduğunu unutmayın .

$k$ değerlerinin oluşturduğu dizi azalmaz:

1 1 1 2 2 2 2 3 3 3 3 4 4 4 6 6 6 6 6 6 ...

ve OEIS'te görünmüyor. Bununla birlikte, tahtanın boyut sırası olan kümülatif versiyonu A139542'dir ( fark etmek için @Arnauld sayesinde ).

Meydan okuma

Girdi : tahtadaki katman sayısını temsil eden pozitif bir tamsayı $S$İsterseniz, giriş olarak S yerine $S-1$ alabilirsiniz ( 0 - endeksli); aşağıya bakınız.$S$$0$

Çıktı : $S$ katmanları olan bir tahtanın ASCII-art gösterimi .

• Çıktı STDOUT veya bir işlev tarafından döndürülen bir argüman aracılığıyla olabilir. Bu durumda, satırsonu olan bir dize, bir 2B karakter dizisi veya bir dize dizisi olabilir.

• Tahtayı temsil etmek için iki karakteri tutarlı bir şekilde seçebilirsiniz .

• Büyüme yönünü tutarlı bir şekilde seçebilirsiniz . Yani, yukarıdaki gösterimler yerine (aşağı ve sağa doğru büyür), yansıyan veya döndürülmüş sürümlerinden herhangi birini üretebilirsiniz.

• Boşluk tahta için kullanılan iki karakterden biri olmadığı sürece, sondaki veya öndeki boşluğa izin verilir (çıktı STDOUT üzerinden ise).

• İsteğe bağlı olarak " $0$ indeksli " girişi kullanabilirsiniz; yani, S katmanları olan bir kartı belirten $S-1$ girişi olarak alın .$S$

Bayt cinsinden en kısa kod kazanır.

Test senaryoları

1:

#

3:

#+#
+#+
#+#

5:

#+#+##
+#+###
#+#+++
+#+#++
##++##
##++##

6:

#+#+##++
+#+###++
#+#+++##
+#+#++##
##++##++
##++##++
++##++##
++##++##

10:

#+#+##++##++###+++
+#+###++##++###+++
#+#+++##++#####+++
+#+#++##++##+++###
##++##++##+++++###
##++##++##+++++###
++##++##++#####+++
++##++##++#####+++
##++##++##++###+++
##++##++##+++++###
++##++##++##+++###
++##++##++##+++###
###+++###+++###+++
###+++###+++###+++
###+++###+++###+++
+++###+++###+++###
+++###+++###+++###
+++###+++###+++###

15:

#+#+##++##++###+++###+++####++++####
+#+###++##++###+++###+++####++++####
#+#+++##++#####+++###+++####++++####
+#+#++##++##+++###+++#######++++####
##++##++##+++++###+++###++++####++++
##++##++##+++++###+++###++++####++++
++##++##++#####+++###+++++++####++++
++##++##++#####+++###+++++++####++++
##++##++##++###+++###+++####++++####
##++##++##+++++###+++#######++++####
++##++##++##+++###+++#######++++####
++##++##++##+++###+++#######++++####
###+++###+++###+++###+++++++####++++
###+++###+++###+++###+++++++####++++
###+++###+++###+++###+++++++####++++
+++###+++###+++###+++###++++####++++
+++###+++###+++###+++#######++++####
+++###+++###+++###+++#######++++####
###+++###+++###+++###+++####++++####
###+++###+++###+++###+++####++++####
###+++###+++###+++###+++++++####++++
+++###+++###+++###+++###++++####++++
+++###+++###+++###+++###++++####++++
+++###+++###+++###+++###++++####++++
####++++####++++####++++####++++####
####++++####++++####++++####++++####
####++++####++++####++++####++++####
####++++####++++####++++####++++####
++++####++++####++++####++++####++++
++++####++++####++++####++++####++++
++++####++++####++++####++++####++++
++++####++++####++++####++++####++++
####++++####++++####++++####++++####
####++++####++++####++++####++++####
####++++####++++####++++####++++####
####++++####++++####++++####++++####

25:

#+#+##++##++###+++###+++####++++##########++++++######++++++######++++++++++++++########++++++++########++++++++########
+#+###++##++###+++###+++####++++##########++++++######++++++######++++++++++++++########++++++++########++++++++########
#+#+++##++#####+++###+++####++++##########++++++######++++++######++++++++++++++########++++++++########++++++++########
+#+#++##++##+++###+++#######++++##########++++++######++++++######++++++++++++++########++++++++########++++++++########
##++##++##+++++###+++###++++####++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
##++##++##+++++###+++###++++####++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
++##++##++#####+++###+++++++####++++++++++######++++++######++++++######++++++++########++++++++########++++++++########
++##++##++#####+++###+++++++####++++++++++######++++++######++++++######++++++++########++++++++########++++++++########
##++##++##++###+++###+++####++++####++++++######++++++######++++++##############++++++++########++++++++########++++++++
##++##++##+++++###+++#######++++####++++++######++++++######++++++##############++++++++########++++++++########++++++++
++##++##++##+++###+++#######++++####++++++######++++++######++++++##############++++++++########++++++++########++++++++
++##++##++##+++###+++#######++++####++++++######++++++######++++++##############++++++++########++++++++########++++++++
###+++###+++###+++###+++++++####++++######++++++######++++++######++++++########++++++++########++++++++########++++++++
###+++###+++###+++###+++++++####++++######++++++######++++++######++++++########++++++++########++++++++########++++++++
###+++###+++###+++###+++++++####++++######++++++######++++++######++++++########++++++++########++++++++########++++++++
+++###+++###+++###+++###++++####++++######++++++######++++++######++++++########++++++++########++++++++########++++++++
+++###+++###+++###+++#######++++##########++++++######++++++######++++++++++++++########++++++++########++++++++########
+++###+++###+++###+++#######++++##########++++++######++++++######++++++++++++++########++++++++########++++++++########
###+++###+++###+++###+++####++++####++++++######++++++######++++++######++++++++########++++++++########++++++++########
###+++###+++###+++###+++####++++####++++++######++++++######++++++######++++++++########++++++++########++++++++########
###+++###+++###+++###+++++++####++++++++++######++++++######++++++######++++++++########++++++++########++++++++########
+++###+++###+++###+++###++++####++++++++++######++++++######++++++######++++++++########++++++++########++++++++########
+++###+++###+++###+++###++++####++++++++++######++++++######++++++######++++++++########++++++++########++++++++########
+++###+++###+++###+++###++++####++++++++++######++++++######++++++######++++++++########++++++++########++++++++########
####++++####++++####++++####++++##########++++++######++++++######++++++########++++++++########++++++++########++++++++
####++++####++++####++++####++++##########++++++######++++++######++++++########++++++++########++++++++########++++++++
####++++####++++####++++####++++##########++++++######++++++######++++++########++++++++########++++++++########++++++++
####++++####++++####++++####++++##########++++++######++++++######++++++########++++++++########++++++++########++++++++
++++####++++####++++####++++####++++######++++++######++++++######++++++########++++++++########++++++++########++++++++
++++####++++####++++####++++####++++######++++++######++++++######++++++########++++++++########++++++++########++++++++
++++####++++####++++####++++####++++++++++######++++++######++++++##############++++++++########++++++++########++++++++
++++####++++####++++####++++####++++++++++######++++++######++++++##############++++++++########++++++++########++++++++
####++++####++++####++++####++++####++++++######++++++######++++++######++++++++########++++++++########++++++++########
####++++####++++####++++####++++####++++++######++++++######++++++######++++++++########++++++++########++++++++########
####++++####++++####++++####++++####++++++######++++++######++++++######++++++++########++++++++########++++++++########
####++++####++++####++++####++++####++++++######++++++######++++++######++++++++########++++++++########++++++++########
######++++++######++++++######++++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
######++++++######++++++######++++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
######++++++######++++++######++++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
######++++++######++++++######++++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
######++++++######++++++######++++++######++++++######++++++######++++++########++++++++########++++++++########++++++++
######++++++######++++++######++++++######++++++######++++++######++++++########++++++++########++++++++########++++++++
++++++######++++++######++++++######++++++######++++++######++++++##############++++++++########++++++++########++++++++
++++++######++++++######++++++######++++++######++++++######++++++##############++++++++########++++++++########++++++++
++++++######++++++######++++++######++++++######++++++######++++++##############++++++++########++++++++########++++++++
++++++######++++++######++++++######++++++######++++++######++++++##############++++++++########++++++++########++++++++
++++++######++++++######++++++######++++++######++++++######++++++##############++++++++########++++++++########++++++++
++++++######++++++######++++++######++++++######++++++######++++++##############++++++++########++++++++########++++++++
######++++++######++++++######++++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
######++++++######++++++######++++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
######++++++######++++++######++++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
######++++++######++++++######++++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
######++++++######++++++######++++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
######++++++######++++++######++++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
++++++######++++++######++++++######++++++######++++++######++++++######++++++++########++++++++########++++++++########
++++++######++++++######++++++######++++++######++++++######++++++######++++++++########++++++++########++++++++########
++++++######++++++######++++++######++++++######++++++######++++++##############++++++++########++++++++########++++++++
++++++######++++++######++++++######++++++######++++++######++++++##############++++++++########++++++++########++++++++
++++++######++++++######++++++######++++++######++++++######++++++##############++++++++########++++++++########++++++++
++++++######++++++######++++++######++++++######++++++######++++++##############++++++++########++++++++########++++++++
######++++++######++++++######++++++######++++++######++++++######++++++########++++++++########++++++++########++++++++
######++++++######++++++######++++++######++++++######++++++######++++++########++++++++########++++++++########++++++++
######++++++######++++++######++++++######++++++######++++++######++++++########++++++++########++++++++########++++++++
######++++++######++++++######++++++######++++++######++++++######++++++########++++++++########++++++++########++++++++
######++++++######++++++######++++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
######++++++######++++++######++++++######++++++######++++++######++++++++++++++########++++++++########++++++++########
++++++######++++++######++++++######++++++######++++++######++++++######++++++++########++++++++########++++++++########
++++++######++++++######++++++######++++++######++++++######++++++######++++++++########++++++++########++++++++########
++++++######++++++######++++++######++++++######++++++######++++++######++++++++########++++++++########++++++++########
++++++######++++++######++++++######++++++######++++++######++++++######++++++++########++++++++########++++++++########
++++++######++++++######++++++######++++++######++++++######++++++######++++++++########++++++++########++++++++########
++++++######++++++######++++++######++++++######++++++######++++++######++++++++########++++++++########++++++++########
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########
########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########++++++++########

Jöle , 40 31 bayt

1SÆD>Ðḟ½ƊṀṭƲ³¡Äż$Ḷ:Ḃ^þ`ʋ/€ḷ""/Y

Çevrimiçi deneyin!

$S-1$

İz bırakmadan Y , tamsayıların bir listesini döndürür, ancak bu meydan okuma için spesifikasyon dışındadır.

açıklama

Bu program üç aşamada çalışır.

1. $k$$k$
2. Bunların her biri için döşeme boyutu ile bir dama tahtası oluşturun$k$
3. Her seferinde bir sonraki panonun sol üst bölümünü mevcut panelle değiştirerek dama tahtası listesinde çalışın.

1. Aşama

1                 | Start with 1
           Ʋ³¡    | Loop through the following the number of times indicated by the first argument to the program; this generates a list of values of k
 S                | - Sum
        Ɗ         | - Following three links as a monad 
  ÆD              |   - List of divisors
    >Ðḟ½          |   - Exclude those greater than the square root
         Ṁ        |   - Maximum
          ṭ       | - Concatenate this to the end of the current list of values of k 
              Äż$ | Zip the cumulative sum of the values of k with the values

2. aşama

      ʋ/€ | For each pair of k and cumulative sum, call the following as a dyad with the cumulative sum of k as the left argument and k as the right (e.g. 15, 3)
Ḷ         | - Lowered range [0, 1 ... , 13, 14]
 :        | - Integer division by k [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4]
  Ḃ       | - Mod 2 [0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]
   ^þ`    | - Outer product using xor function and same argument to both side

Sahne 3

   /  | Reduce using the following:
ḷ""   | - Replace the top left portion of the next matrix with the current one
    Y | Finally join by newlines

Tuval , 34 32 bayt

０#０⁸［#+¶+#ｘｘ＊ｙｘ＋ｍ⤢αｍ；ｎｌｗ√｛ｙ；％‽²Ｘ

Burada deneyin!

Python 2 , 217 215212 bayt

def f(x):
 b=['1'];n=1
 for i in range(x):P=max(j*(n%j<(j<=n**.5))for j in range(1,1+n));n+=P;b=[l+P*`j/P%2^i%2`for j,l in enumerate(b)];s=len(b[0]);b+=[((v*P+`1^int(v)`*P)*s)[:s]for v in b[0][len(b):]]
 return b

Çevrimiçi deneyin!

0 dizinli, karakterler olarak 0ve kullanır1

Python 2 , 184 178 176 169 bayt

def h(j,a=['1'],R=range):
 for i in R(j):L=len(a);k=max(x for x in R(1,L+1)if(x*x<=L)>L%x);a=[a[m]+k*`(i+m/k)%2`for m in R(L)]+[((`i%2`*k+`~i%2`*k)*L)[:L+k]]*k
 return a

Çevrimiçi deneyin!

Kullanımları 1, 0için #, -; 0-indexing kullanır .

JavaScript (ES7), 164 bayt

Giriş 0 dizinlidir. İle bir matris çıkarır$0$için #ve$1$için +.

n=>(b=[1],g=(a,w,d=w**.5|0)=>b[n]?a:w%d?g(a,w,d-1):g(a.concat(Array(d).fill(b.push(d)&&i++)),w+d))([0],i=1).map((_,y,a)=>a.map((_,x)=>(x/b[v=a[x>y?x:y]]^y/b[v])&1))

Çevrimiçi deneyin!

Kömür , 37 bayt

ＦＮ«≔⊕⌈Φ₂⊕Ｌυ¬﹪Ｌυ⊕κηＦη«ＰL⭆⊞Ｏυω§#+÷⁻κμη↙

Çevrimiçi deneyin! Bağlantı, kodun ayrıntılı versiyonudur. 1 endeksli. Çıktı aşağı ve sol büyür (aşağı ve sağ ekstra bir bayt maliyeti, ancak aynı bayt sayısı için büyüyebilir). Açıklama:

ＦＮ«

döngü $S$ zamanlar.

≔⊕⌈Φ₂⊕Ｌυ¬﹪Ｌυ⊕κη

Hesaplamak $k\leq\sqrt{n+1}$. Bu sadece$n=0$ bu durumda bu formül $k=1$.

Ｆη«

döngü $k$ kez, her yeni satır ve sütun için bir kez.

ＰL⭆⊞Ｏυω§#+÷⁻κμη

Çıktı satır ve sütun arasındaki alternatif emin olmak #ve +bu şekilde karakterler #(diyagonal dışarıya dan çünkü bizler çizim) dizenin sonunda bir sınır olduğunu ancak her zaman ilk karakterdir. ⊞Ｏυωher satırı her seferinde bir karakter daha uzun yapar, bu da$n$ uzunluk olarak.

↙

Bir sonraki sıra için aşağı ve sola hareket edin.

05AB1E , 43 42 bayt

$G©ÐX‚ˆÑʒ®>t‹}àDU+}¯εÝ`θ÷ɨDδ^}RζεðKζðδK€θ

Esinlenerek @NickKennedy Jelly yanıt ve arka kısmı, ζεðKζðδK€θbir liman @Emigna 'burada s 05AB1E cevap .

Bir matris döndürür 0yerine #ve 1yerine +.

Çevrimiçi deneyin veya ilkini çıkararak çevrimiçi deneyin$[2,n]$sonuçlar ( J,altbilgi ve --no-lazybayrak sonuçtaki matrisi güzel yazdırmak içindir).

Açıklama:

$                # Push 1 and the input
 G               # Loop the input - 1 amount of times:
  ©              #  Store the top of the stack in variable `r` (without popping)
   Ð             #  And triplicate the top as well
    X‚           #  Pair it with variable `X` (which is 1 by default)
      ˆ          #  And pop and store this pair in the global array
    Ñ            #  Get the divisors of the integer we triplicated
     ʒ    }à     #  Get the highest divisor which is truthy for:
         ‹       #   Where the divisor integer is smaller than
      ®>t        #   the square root of `r+1`
            DU   #  Store a copy of this largest filtered divisor as new variable `X`
              +  #  And add it to the triplicated integer
 }¯              # After the loop: push the global array
   ε             # Map each pair to:
    Ý θ          #  Convert the first value in the pair to a list in the range [0,n]
     `           #  and push both this list and the second value to the stack
       ÷         # Integer-divide each value in the list by the second value
        É        # Check for each value if it's even (1 if even; 0 if odd)
         ¨       # Remove the last item
          Dδ     # Loop double vectorized over this list:
            ^    #  And XOR the values with each other
   }R            # After the map: reverse the list of digit-matrices
     ζ           # Zip/transpose; swapping rows and columns, with a space as filler
      ε          # map each matrix to:
       ðK        #  Remove all spaces from the current matrix
         ζ       #  Zip/transpose with a space as filler again
          ðδK    #  Deep remove all spaces
             €θ  #  Then only leave the last values of each row
                 # (after which the resulting matrix of 0s and 1s is output implicitly)

Haskell'in 149 146 bayt

(iterate g["#"]!!)
g b|let e=(<$[1..d]);l=length b;d=last[i|i<-[1..l],i*i<=l,mod l i<1];m="+#"++m=(e$take(l+d)$e=<<'#':m)++zipWith(++)(e=<<e<$>m)b

Bu 0 indekslenir, bir dize listesi döndürür ve yukarı ve sola doğru büyür.

Çevrimiçi deneyin!

(iterate g["#"]!!)                    -- start with ["#"], repeatedly add a layer
                                      -- (via function 'g'), collect all results in
                                      -- a list and index it with the input number

g b | let                             -- add a single layer to chessboard 'b'

 l=length b                           -- let 'l' be the size of 'b'
 d=last[i|i<-[1..l],i*i<=l,mod l i<1] -- let 'd' be the size of the new layer
 e=(<$[1..d])                         -- let 'e' be a functions that makes 'd'
                                      --   copies of it's argument
 m="#+"++m                            -- let 'm' be an infinite string of "+#+#+..."

 =                                    -- return
              zipWith(++)             --   concatenate pairwise
                         (e=<<e<$>m)  --   a list of squares made by expanding each
                                      --   char in 'm' to size 'd'-by-'d'
                                    b --   and 'b' (zipWith truncates the infinite
                                      --   list of squares to the length of 'b')
                                      --
           ++                         --   and prepend
                                      --
(e$take(l+d)$e=<<'#':m)               --   the top layer, i.e. a list of 'd' strings
                                      --   each with the pattern 'd' times '#'
                                      --   followed by 'd' times '+', etc., each
                                      --   shortened to the correct size of 'l'+'g'

Perl 6 , 156 144 155 154 bayt

+ 11 nimi tarafından bildirilen bir hatayı düzeltmek için.

{$!=-1;join "
",(1,{my \k=max grep $_%%*,1.. .sqrt;++$!;flat .kv.map(->\i,\l {l~($!+i/k)%2+|0 x k}),substr(($!%2 x k~1-$!%2 x k)x$_,0,$_+k)xx k}...*)[$_]}

Kabaca Chas Brown'un Python çözümüne dayanıyor . S'yi sıfır indeksli olarak alır. Çıktılar 0ve 1.

Çevrimiçi deneyin!