A221643 Numbers k such that k^2 XOR (k+1)^2 is a square, where XOR is the bitwise XOR operator.

0, 3, 4, 23, 24, 43, 44, 76, 111, 112, 115, 139, 164, 180, 183, 248, 264, 323, 327, 348, 411, 479, 480, 499, 611, 699, 747, 787, 943, 976, 1072, 1103, 1111, 1176, 1268, 1388, 1447, 1576, 1684, 1851, 1983, 1984, 2008, 2243, 2692, 3271, 3383, 3452, 3464, 3532, 3679, 3804, 3867

Offset: 1

Author

Alex Ratushnyak, Mar 27 2013

Keywords

• nonn
• base

Crossrefs

Cf. A145827, A001737.

Programs

Python

import math
for i in range(1<<16):
    s = (i*i) ^ ((i+1)*(i+1))
    t = int(math.sqrt(s))
    if s == t*t:
        print(str(i), end=',')