A226472 Numbers n such that n^2 XOR triangular(n) is a perfect square. XOR is the bitwise logical exclusive-or operator.

0, 1, 6, 8, 4086, 24136, 162297, 7868054, 29792904, 22666693375

Offset: 1

Author

Alex Ratushnyak, Jun 08 2013

Keywords

• nonn
• more
• base

Comments

Indices of perfect squares in A226470. No other terms below 2^35. Roots of generated squares: 0, 0, 7, 10, 2915, 29506, 149434, 6328037, 27602118, 20243443647.

Examples

			8^2 XOR triangular(8) = 64 XOR 36 = 100, because 100 is a perfect square, 8 is in the sequence.
		

Crossrefs

Cf. A000217, A000290, A226470, A221643.

Programs

C

#include 
#include 
int main() {
  for (unsigned long long a, r, n=0; n < (1ULL<<32); ++n) {
    a = (n*n) ^ (n*(n+1)/2);
    r = sqrt(a);
    if (r*r==a)  printf("%llu, ", n);
  }
  return 0;
}