A226146 Numbers n such that n^2 is an average of three successive primes.

49, 161, 219, 351, 363, 469, 575, 597, 671, 877, 909, 933, 1013, 1225, 1231, 1303, 1359, 1381, 1419, 1489, 1577, 1653, 1797, 1815, 1989, 2083, 2117, 2177, 2241, 2289, 2301, 2403, 2483, 2493, 2517, 2611, 2617, 2653, 2727, 2779, 2869, 2931, 3029, 3051, 3261, 3515, 3617

Offset

1,1

Links

Table of n, a(n) for n=1..47.

Mathematica

Select[Sqrt[Mean[#]]&/@Partition[Prime[Range[10^6]], 3, 1], IntegerQ] (* Harvey P. Dale, Oct 23 2021 *)

Prog

(C)
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define TOP (1ULL<<30)
int main() {
  unsigned long long i, j, p1, p2, r, s;
  unsigned char *c = (unsigned char *)malloc(TOP/8);
  memset(c, 0, TOP/8);
  for (i=3; i < TOP; i+=2)
    if ((c[i>>4] & (1<<((i>>1) & 7)))==0 /*&& i<(1ULL<<32)*/)
        for (j=i*i>>1; j<TOP; j+=i)  c[j>>3] |= 1 << (j&7);
  for (p2=2, p1=3, i=5; i < TOP; i+=2)
    if ((c[i>>4] & (1<<((i>>1) & 7)))==0) {
      s = p2 + p1 + i;
      if ((s%3)==0) {
        s/=3;
        r = sqrt(s);
        if (r*r==s) printf("%llu, ", r);
      }
      p2 = p1, p1 = i;
    }
  return 0;
}

Crossrefs

Cf. A076304, A206279, A226145-A226150.

Sequence in context: A044762 A159247 A265423 * A339730 A338011 A066551

Adjacent sequences: A226143 A226144 A226145 * A226147 A226148 A226149

Keyword

nonn

Author

Alex Ratushnyak, May 28 2013

Status

approved