A226153 Numbers n such that triangular(n) is an average of 4 consecutive primes.

5, 10, 14, 15, 22, 34, 49, 54, 64, 66, 81, 93, 104, 116, 121, 122, 146, 154, 156, 180, 194, 221, 222, 236, 270, 299, 320, 332, 334, 337, 346, 360, 369, 371, 374, 387, 416, 417, 429, 435, 444, 472, 492, 498, 511, 520, 551, 556, 617, 622, 637, 654, 657, 670, 674, 677, 680

Offset

1,1

Links

Zak Seidov, Table of n, a(n) for n = 1..3000

Maple

A034963 := proc(n)
    add(ithprime(i), i=n..n+3) ;
end proc:
istriangular:=proc(n) local t1; t1:=floor(sqrt(2*n)); if n = t1*(t1+1)/2 then return t1 ; else return -1; end if; end;
for n from 1 to 90000 do
    s := A034963(n)/4 ;
    if type(s, 'integer') then
    tr := istriangular(s) ;
    if tr >= 0  then
        printf("%d, ", tr) ;
    end if;
    end if;
end do: # R. J. Mathar, Jun 06 2013

Mathematica

Module[{nn=30000, ntrs, m}, ntrs=Table[{n, (n(n+1))/2}, {n, nn}]; m=Mean/@Partition[Prime[ Range[ nn]], 4, 1]; Select[ntrs, MemberQ[m, #[[2]]]&]][[;; , 1]] (* Harvey P. Dale, Jun 08 2023 *)

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, ", r);
      }
      p3 = p2, p2 = p1, p1 = i;
    }
  return 0;
}

Crossrefs

Cf. A102655, A226151.

Sequence in context: A313451 A164889 A173553 * A275991 A313452 A023981

Adjacent sequences: A226150 A226151 A226152 * A226154 A226155 A226156

Keyword

nonn

Author

Alex Ratushnyak, May 28 2013

Status

approved