A226102 Prime powers (A025475) representable as triangular(k)+1.

1, 4, 16, 121, 529, 4096, 139129, 160554241, 812293020529, 379188080252621270252095321

Offset: 1

Author

Alex Ratushnyak, May 26 2013

Keywords

• nonn
• more

Comments

Indices of triangular numbers are in A226103.

53072032161200090602953513048447623^2 is also a term. - Giovanni Resta, May 26 2013

Crossrefs

Cf. A025475, A000217, A226103.

Programs

C

#include 
#include 
#include 
#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("1, "), 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, ", j);
        double k = ((double)j) * ((double)p);
        if (k >= ((double)(1ULL<<62)*4.0)) break;
      }
      if (i>1) for (j=i*i>>1; j>3] |= 1 << (j&7);
    }
  // SORT the output
  return 0;
}

Formula

a(n) = A000217(A226103(n)) + 1.

Extensions

a(10) from Giovanni Resta, May 26 2013