A226103 Numbers n such that triangular(n)+1 is a prime power (A025475).

0, 2, 5, 15, 32, 90, 527, 17919, 1274592, 27538630330959

Offset

1,2

Comments

Generated prime powers are in A226102.

75055187665070250755513356704300447 is also a term. - Giovanni Resta, May 26 2013

Links

Table of n, a(n) for n=1..10.

Formula

A000217(a(n)) + 1 = a(n) * (a(n)+1) / 2 + 1 = A226102(n).

Prog

(C)
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define TOP (1ULL<<32)  // Memory usage: 0.5 Gb
int main() {
  unsigned long long i, j, p, t, r;
  unsigned char *c = (unsigned char *)malloc(TOP/8);
  memset(c, 0, TOP/8);
  for (printf("0, "), i=1; i < TOP; i+=2)
    if ((c[i>>4] & (1<<((i>>1)&7))) == 0) {
      for (p = i + (i==1), j = p*p; ; j*=p) {
        t = j - 1;
        r = sqrt(t*2);
        if (r*(r+1)==t*2)  printf("%llu, ", r);
        double k = ((double)j) * ((double)p);
        if (k >= ((double)(1ULL<<62)*4.0)) break;
      }
      if (i>1) for (j=i*i>>1; j<TOP; j+=i)  c[j>>3] |= 1 << (j&7);
    }
  // SORT the output
  return 0;
}

Crossrefs

Cf. A025475, A000217, A226102.

Sequence in context: A034499 A299159 A006451 * A000962 A118387 A245961

Adjacent sequences: A226100 A226101 A226102 * A226104 A226105 A226106

Keyword

nonn,more

Author

Alex Ratushnyak, May 26 2013

Extensions

a(10) from Giovanni Resta, May 26 2013

Status

approved