A226155 Smallest of four consecutive primes whose average is a triangular number.

11, 47, 101, 109, 241, 587, 1217, 1481, 2069, 2203, 3313, 4357, 5443, 6779, 7351, 7489, 10723, 11927, 12239, 16267, 18911, 24517, 24733, 27953, 36571, 44839, 51347, 55249, 55931, 56941, 60017, 64951, 68239, 68993, 70117, 75041, 86719, 87133, 92227, 94819, 98773, 111611

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Maple

A000217inv:=proc(n) local t1; t1:=floor(sqrt(2*n)); if n = t1*(t1+1)/2 then return t1 ; else return -1; end if; end;
isA226155 := proc(n)
    local p1, p2, p3, a102655 ;
    if isprime(n) then
        p1 := nextprime(n) ;
        p2 := nextprime(p1) ;
        p3 := nextprime(p2) ;
        a102655 := (n+p1+p2+p3)/4 ;
        if type(a102655, 'integer') then
            if A000217inv(a102655) >= 0 then
                return true;
            else
                return false;
            end if;
        else
            return false;
        end if;
    else
        false;
    end if;
end proc:
for n from 1 do
    p := ithprime(n) ;
    if isA226155(p) then
        printf("%d, \n", p) ;
    end if;
end do: # R. J. Mathar, Jun 06 2013

Prog

(C)
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define TOP (1ULL<<30)
int main() {
  unsigned long long i, j, p1, p2, p3, 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 (p3=2, p2=3, p1=5, i=7; i < TOP; i+=2)
    if ((c[i>>4] & (1<<((i>>1) & 7)))==0) {
      s = p3 + p2 + p1 + i;
      if (s%4==0) {
        s/=4;
        r = sqrt(s*2);
        if (r*(r+1)==s*2) printf("%llu, ", p3);
      }
      p3 = p2, p2 = p1, p1 = i;
    }
  return 0;
}

Crossrefs

Cf. A102655, A226151 A226153, A226154.

Sequence in context: A142103 A031910 A009941 * A107149 A158463 A143830

Adjacent sequences: A226152 A226153 A226154 * A226156 A226157 A226158

Keyword

nonn

Author

Alex Ratushnyak, May 28 2013

Status

approved