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A226151 Numbers n such that triangular(n) is a sum of 4 consecutive primes. 4
8, 15, 39, 56, 60, 144, 155, 203, 212, 216, 263, 388, 451, 464, 480, 555, 619, 644, 680, 723, 736, 788, 791, 799, 876, 903, 1012, 1056, 1143, 1239, 1284, 1368, 1479, 1547, 1611, 1684, 1695, 1703, 1827, 1859, 1908, 1939, 2100, 2108, 2135, 2148, 2152, 2187, 2199, 2216 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..500

MAPLE

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;

A034963 := proc(n)

    add(ithprime(i), i=n..n+3) ;

end proc:

for n from 1 to 90000 do

    ist := istriangular(A034963(n)) ;

    if ist >= 0 then

        printf("%d, ", ist) ;

    end if;

end do: # R. J. Mathar, Jun 04 2013

MATHEMATICA

(Sqrt[8#+1]-1)/2&/@Select[Total/@Partition[Prime[Range[ 60000]], 4, 1], OddQ[ Sqrt[8#+1]]&] (* Harvey P. Dale, Apr 06 2016 *)

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;

      r = sqrt(s*2);

      if (r*(r+1)==s*2) printf("%llu, ", r);

      p3 = p2, p2 = p1, p1 = i;

    }

  return 0;

}

CROSSREFS

Cf. A000217, A034963, A051395, A206280, A226154.

Sequence in context: A343141 A197602 A306599 * A253767 A254541 A137658

Adjacent sequences:  A226148 A226149 A226150 * A226152 A226153 A226154

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, May 28 2013

STATUS

approved

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Last modified August 2 20:05 EDT 2021. Contains 346428 sequences. (Running on oeis4.)