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 A145768 a(n) = the bitwise XOR of squares of first n natural numbers. 10
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Up to n=10^8, a(15) is the only zero term and a(1)=a(9) are the only terms for which a(n)=1. Can it be proved that any number can only appear a finite number of times in this sequence? [M. F. Hasler, Oct 20 2008] Even terms occur at A014601, odd terms at A042963; A010873(a(n))=A021913(n+1). - Reinhard Zumkeller, Jun 05 2012 If squares occur, they must be at indexes != 2 or 5 (mod 8). - Roderick MacPhee, Jul 17 2017 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 StackExchange, Perfect squares in a XOR-Sum of perfect squares FORMULA a(n)=1^2 xor 2^2 xor ... xor n^2. 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 MATHEMATICA Rest@ FoldList[BitXor, 0, Array[#^2 &, 50]] PROG (PARI) an=0; for( i=1, 50, print1(an=bitxor(an, i^2), ", ")) \\ M. F. Hasler, Oct 20 2008 (PARI) al(n)=local(m); vector(n, k, m=bitxor(m, k^2)) (Haskell) import Data.Bits (xor) a145768 n = a145768_list !! n a145768_list = scanl1 xor a000290_list -- Reinhard Zumkeller, Jun 05 2012 (Python) from operator import xor def A145768(n): ....return reduce(xor, [x**2 for x in range(n+1)]) # Chai Wah Wu, Aug 08 2014 CROSSREFS Cf. A003815, A145827, A145828, A145829, A145830, A145831. [M. F. Hasler, Oct 20 2008] Cf. A193232. Cf. A000290. Sequence in context: A128439 A240187 A172426 * A162778 A160807 A038376 Adjacent sequences: A145765 A145766 A145767 * A145769 A145770 A145771 KEYWORD easy,nonn,base,look AUTHOR Vladimir Reshetnikov, Oct 18 2008 STATUS approved

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Last modified August 10 21:39 EDT 2024. Contains 375058 sequences. (Running on oeis4.)