A145768 a(n) = the bitwise XOR of squares of first n natural numbers.
0, 1, 5, 12, 28, 5, 33, 16, 80, 1, 101, 28, 140, 37, 225, 0, 256, 33, 357, 12, 412, 37, 449, 976, 400, 993, 325, 924, 140, 965, 65, 896, 1920, 961, 1861, 908, 1692, 965, 1633, 912, 1488, 833, 1445, 668, 1292, 741, 2721, 512, 2816, 609, 2981, 396, 2844, 485
Offset: 0
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
- StackExchange, Perfect squares in a XOR-Sum of perfect squares
Crossrefs
Programs
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Haskell
import Data.Bits (xor) a145768 n = a145768_list !! n a145768_list = scanl1 xor a000290_list -- Reinhard Zumkeller, Jun 05 2012
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Maple
A[0]:= 0: for n from 1 to 100 do A[n]:= Bits:-Xor(A[n-1],n^2) od: seq(A[i],i=0..100); # Robert Israel, Dec 08 2019
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Mathematica
Rest@ FoldList[BitXor, 0, Array[#^2 &, 50]]
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PARI
an=0; for( i=1,50, print1(an=bitxor(an,i^2),",")) \\ M. F. Hasler, Oct 20 2008
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PARI
al(n)=local(m);vector(n,k,m=bitxor(m,k^2))
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Python
from functools import reduce from operator import xor def A145768(n): return reduce(xor, [x**2 for x in range(n+1)]) # Chai Wah Wu, Aug 08 2014
Formula
a(n)=1^2 xor 2^2 xor ... xor n^2.
Comments