A220518 Numbers n such that A193232(n) is a triangular number.

0, 1, 5, 9, 45, 49, 101, 153, 1569, 7163, 7171, 8162, 18974, 18976, 24467, 33490, 60290, 63046, 359539, 551494, 1769418, 2813691, 4140392, 4649729, 6675935, 9653486, 59131393, 158169499, 243345386, 588183781, 1315697727, 1387290631, 1522472645, 1879098546

Offset

1,3

Comments

Numbers k such that bitwise XOR of first k triangular numbers is a triangular number.

Links

Table of n, a(n) for n=1..34.

Prog

(C)
#include <stdio.h>
typedef unsigned long long U64;
U64 rootTriangular(U64 a) {
    U64 sr = 1L<<32, s, b;
    if (a < (sr/2)*(sr+1)) {
      sr>>=1;
      while (a < sr*(sr+1)/2)  sr>>=1;
    }
    for (b = sr>>1; b; b>>=1) {
        s = sr+b;
        if (a >= s*(s+1)/2)  sr = s;
    }
    return sr;
}
int main() {
  U64 a=0, i, t;
  for (i=0; i < 1L<<32; ++i) {
      a ^= i*(i+1)/2;
      t = rootTriangular(a);
      if (a == t*(t+1)/2)  printf("%llu\n", i);
  }
  return 0;
}

Crossrefs

Cf. A193232.

Cf. A145827 (bitwise XOR of first k squares is a square).

Sequence in context: A226065 A321718 A304127 * A145031 A121724 A149496

Adjacent sequences: A220515 A220516 A220517 * A220519 A220520 A220521

Keyword

base,nonn

Author

Alex Ratushnyak, Mar 27 2013

Status

approved