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%I #5 May 29 2013 12:16:50
%S 193,233,265,301,526,709,753,922,961,962,986,1126,1178,1285,1373,1485,
%T 1525,1537,1558,1601,1710,1737,1962,1965,2202,2437,2466,2578,2685,
%U 2693,2862,3206,3346,3462,3622,3682,3937,3938,3965,4005,4017,4018,4058,4393,4489,4498,4717
%N Numbers n such that triangular(n) is an average of three successive primes.
%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 if ((s%3)==0) {
%o s/=3;
%o r = sqrt(s*2);
%o if (r*(r+1)==s*2) printf("%llu, ", r);
%o }
%o p2 = p1, p1 = i;
%o }
%o return 0;
%o }
%Y Cf. A076304, A206279, A226145-A226150.
%K nonn
%O 1,1
%A _Alex Ratushnyak_, May 28 2013
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