cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A193232 Bitwise XOR of first n triangular numbers.

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%I A193232 #20 Feb 19 2023 17:35:57
%S A193232 0,1,2,4,14,1,20,8,44,1,54,116,58,97,8,112,248,97,202,116,166,65,188,
%T A193232 424,132,449,158,484,114,449,16,480,1008,449,914,484,894,449,804,40,
%U A193232 796,65,966,116,938,1953,920,2032,872,1953,858,1652,790,1665,844,1352
%N A193232 Bitwise XOR of first n triangular numbers.
%H A193232 John Tyler Rascoe, <a href="/A193232/b193232.txt">Table of n, a(n) for n = 0..10000</a>
%p A193232 a:= proc(n) option remember; `if`(n=0, 0,
%p A193232       Bits[Xor](a(n-1), n*(n+1)/2))
%p A193232     end:
%p A193232 seq(a(n), n=0..55);  # _Alois P. Heinz_, Feb 19 2023
%t A193232 Module[{nn=60,trs},trs=Accumulate[Range[nn]];Table[BitXor@@Take[trs,n],{n,0,nn}]] (* _Harvey P. Dale_, Dec 15 2017 *)
%o A193232 (PARI) al(n) = local(m); vector(n,k,m=bitxor(m,k*(k+1)\2))
%o A193232 (Python)
%o A193232 from operator import xor
%o A193232 from functools import reduce
%o A193232 def A193232(n): return reduce(xor, (x*(x+1) for x in range(n+1)))//2 # _Chai Wah Wu_, Dec 16 2021
%Y A193232 Cf. A000217, A145768, A003815.
%K A193232 nonn
%O A193232 0,3
%A A193232 _Franklin T. Adams-Watters_, Jul 18 2011