A226148 - OEIS

%I #13 Oct 18 2021 11:16:56

%S 2,3,619,1123,3373,4603,6829,9067,18973,25933,29179,29741,33211,40583,

%T 48313,72923,74923,117991,130973,202201,231067,253993,255217,267317,

%U 291491,339139,346309,363829,423191,449621,476279,489337,519487,533713,539093,592507,602603,621133

%N Smallest of three consecutive primes whose sum is a triangular number.

%H Robert Israel, <a href="/A226148/b226148.txt">Table of n, a(n) for n = 1..2300</a>

%p R:= 2: count:= 1:

%p for k from 1 while count < 100 do

%p  for j from 1 to 2 do

%p   m:= 4*k+j;

%p   x:= m*(m+1)/2;

%p   q= prevprime(ceil(x/3));

%p   p:= prevprime(q); r:= nextprime(q);

%p   t:= p+q+r;

%p   if t < x then while t < x do p:= q; q:= r; r:= nextprime(r); t:=p+q+r od

%p   elif t > x then while t > x do r:= q; q:= p; p:= prevprime(p); t:= p+q+r od

%p   fi;

%p   if t = x then  R:= R,p; count:= count+1; fi

%p od od :

%p R; # _Robert Israel_, Oct 18 2021

%o (C)

%o #include <stdio.h>

%o #include <stdlib.h>

%o #include <math.h>

%o #define TOP (1ULL<<30)

%o int main() {

%o   unsigned long long i, j, p1, p2, r, s;

%o   unsigned char *c = (unsigned char *)malloc(TOP/8);

%o   memset(c, 0, TOP/8);

%o   for (i=3; i < TOP; i+=2)

%o     if ((c[i>>4] & (1<<((i>>1) & 7)))==0 /*&& i<(1ULL<<32)*/)

%o         for (j=i*i>>1; j<TOP; j+=i)  c[j>>3] |= 1 << (j&7);

%o   for (p2=2, p1=3, i=5; i < TOP; i+=2)

%o     if ((c[i>>4] & (1<<((i>>1) & 7)))==0) {

%o       s = p2 + p1 + i;

%o       r = sqrt(s*2);

%o       if (r*(r+1)==s*2) printf("%llu, ", p2);

%o       p2 = p1, p1 = i;

%o     }

%o   return 0;

%o }

%Y Cf. A076304, A206279, A226145, A226146, A226147, A226149, A226150.

%Y Cf. A167788 (the resulting triangular numbers).

%K nonn

%O 1,1

%A _Alex Ratushnyak_, May 28 2013