A226154 Smallest of four consecutive primes whose sum is a triangular number.

5, 23, 191, 389, 449, 2593, 3011, 5167, 5639, 5851, 8669, 18839, 25463, 26953, 28843, 38561, 47963, 51907, 57859, 65419, 67789, 77711, 78301, 79889, 96013, 102023, 128119, 139501, 163417, 192037, 206233, 234083, 273601, 299329, 324593, 354677, 359323, 362723, 417451

Offset: 1

Author

Alex Ratushnyak, May 28 2013

Keywords

• nonn

Crossrefs

Cf. A034963, A226151.

Programs

C

#include 
#include 
#include 
#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>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;
      r = sqrt(s*2);
      if (r*(r+1)==s*2) printf("%llu, ", p3);
      p3 = p2, p2 = p1, p1 = i;
    }
  return 0;
}

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;
isA226154 := proc(n)
    local p1,p2,p3,a034963 ;
    if isprime(n) then
        p1 := nextprime(n) ;
        p2 := nextprime(p1) ;
        p3 := nextprime(p2) ;
        a034963 := n+p1+p2+p3 ;
        if A000217inv(a034963) >= 0 then
            return true;
        else
            return false;
        end if;
    else
        false;
    end if;
end proc:
for n from 1 do
    p := ithprime(n) ;
    if isA226154(p) then
        printf("%d,\n",p) ;
    end if;
end do: # R. J. Mathar, Jun 06 2013