A225536 Numbers of triples {x, y, z} such that z >= y > 1 and prime(x) + prime(y) * prime(z) = 2^n.

0, 0, 0, 0, 1, 4, 5, 15, 22, 43, 65, 131, 204, 387, 635, 1136, 2048, 3727, 6794, 12296, 22601, 41746, 76778, 141923, 263414, 491925, 917269, 1718985, 3225496, 6067030, 11435208, 21593415, 40858139

Offset

0,6

Links

Table of n, a(n) for n=0..32.

Example

2^4 = 16 = 7 + 3*3, so a(4) = 1.
2^5 = 32 = 7 + 5*5 = 11 + 3*7 = 17 + 3*5 = 23 + 3*3, so a(5) = 4.

Prog

(C)
#include <stdio.h>
#include <math.h>
#define TOP (1ULL<<32)
int main() {
  unsigned long long i, j, k, n, pp = 0, x, px, y, py, sr;
  unsigned int *primes = (unsigned int*)malloc(TOP/4);
  char *c = (char*)malloc(TOP/2);
  memset(c, 0, TOP/2);
  for (c[0] = i = 3; i < TOP; i+=2)
    if (c[i>>1]==0)
      for (primes[pp++]=i, j=i*i>>1; j<TOP/2; j+=i)  c[j]=1;
  for (n = 1; n <= TOP; n+=n) {
    for (k = x = 0; x < pp && (px = primes[x]) < n; ++x) {
      for (i=n-px, sr=sqrt(i), y=0; (py=primes[y])<=sr; ++y)
        if (i % py == 0) { if (c[i/py>>1] == 0) ++k; break; }
    }
    printf("%llu, ", k);
  }
}

Crossrefs

Cf. A000040, A006307, A225437.

Sequence in context: A037955 A225121 A267991 * A084179 A026634 A026656

Adjacent sequences: A225533 A225534 A225535 * A225537 A225538 A225539

Keyword

nonn,more

Author

Alex Ratushnyak, May 10 2013

Status

approved