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

Offset: 1

Author

Alex Ratushnyak, Jun 08 2013

Keywords

• nonn
• base

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, ...

Crossrefs

Cf. A000217, A000290, A226470, A224218.

Programs

Mathematica

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

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, end=', ')