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A226149
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Smallest of three consecutive primes whose average is a square.
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3
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2393, 25913, 47951, 123191, 131759, 219953, 330611, 356387, 450227, 769117, 826271, 870479, 1026143, 1500613, 1515347, 1697797, 1846861, 1907141, 2013541, 2217107, 2486873, 2732383, 3229189, 3294191, 3956101, 4338871, 4481677, 4739297, 5022067, 5239511, 5294591, 5774387
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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Select[Partition[Prime[Range[400000]], 3, 1], IntegerQ[Sqrt[Mean[#]]]&][[All, 1]] (* Harvey P. Dale, Jan 10 2021 *)
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PROG
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(C)
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define TOP (1ULL<<30)
int main() {
unsigned long long i, j, p1, p2, 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 (p2=2, p1=3, i=5; i < TOP; i+=2)
if ((c[i>>4] & (1<<((i>>1) & 7)))==0) {
s = p2 + p1 + i;
if ((s%3)==0) {
s/=3;
r = sqrt(s);
if (r*r==s) printf("%llu, ", p2);
}
p2 = p1, p1 = i;
}
return 0;
}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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