A226471 - OEIS

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A226471

Numbers n such that n^2 XOR triangular(n) is a triangular number. XOR is the bitwise logical exclusive-or operator.

0, 1, 3, 7, 15, 25, 31, 63, 113, 127, 189, 200, 255, 381, 481, 499, 511, 765, 1004, 1011, 1023, 1533, 1785, 1808, 1985, 2023, 2035, 2047, 3069, 3199, 3255, 3577, 3810, 4071, 4083, 4095, 4446, 6141, 6399, 7161, 8065, 8135, 8167, 8179, 8191, 12285, 12799, 14279, 14280

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OFFSET

1,3

COMMENTS

Indices of triangular numbers in A226470. Numbers n such that A226470(n) and A226470(n+1) are triangular numbers: 0, 14279, 491279, 16251935, 29358023, 528478271, ...

LINKS

Table of n, a(n) for n=1..49.

MATHEMATICA

Select[Range[0, 15000], OddQ[Sqrt[8*BitXor[#^2, (#(#+1))/2]+1]]&] (* Harvey P. Dale, Jul 22 2024 *)

PROG

(Python)

import math

for n in range(100000000):

a = (n*n) ^ (n*(n+1)/2)

r = int(math.sqrt(a*2))

if r*(r+1)==a*2: print n,

CROSSREFS