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%I #8 Apr 06 2016 12:31:44
%S 8,15,39,56,60,144,155,203,212,216,263,388,451,464,480,555,619,644,
%T 680,723,736,788,791,799,876,903,1012,1056,1143,1239,1284,1368,1479,
%U 1547,1611,1684,1695,1703,1827,1859,1908,1939,2100,2108,2135,2148,2152,2187,2199,2216
%N Numbers n such that triangular(n) is a sum of 4 consecutive primes.
%H Harvey P. Dale, <a href="/A226151/b226151.txt">Table of n, a(n) for n = 1..500</a>
%p 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;
%p A034963 := proc(n)
%p add(ithprime(i),i=n..n+3) ;
%p end proc:
%p for n from 1 to 90000 do
%p ist := istriangular(A034963(n)) ;
%p if ist >= 0 then
%p printf("%d,",ist) ;
%p end if;
%p end do: # _R. J. Mathar_, Jun 04 2013
%t (Sqrt[8#+1]-1)/2&/@Select[Total/@Partition[Prime[Range[ 60000]],4,1], OddQ[ Sqrt[8#+1]]&] (* _Harvey P. Dale_, Apr 06 2016 *)
%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, p3, 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 (p3=2, p2=3, p1=5, i=7; i < TOP; i+=2)
%o if ((c[i>>4] & (1<<((i>>1) & 7)))==0) {
%o s = p3 + p2 + p1 + i;
%o r = sqrt(s*2);
%o if (r*(r+1)==s*2) printf("%llu, ", r);
%o p3 = p2, p2 = p1, p1 = i;
%o }
%o return 0;
%o }
%Y Cf. A000217, A034963, A051395, A206280, A226154.
%K nonn
%O 1,1
%A _Alex Ratushnyak_, May 28 2013
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