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 A226149 Smallest of three consecutive primes whose average is a square. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS MATHEMATICA Select[Partition[Prime[Range[400000]], 3, 1], IntegerQ[Sqrt[Mean[#]]]&][[All, 1]] (* Harvey P. Dale, Jan 10 2021 *) PROG (C) #include #include #include #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>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; } CROSSREFS Cf. A076304, A206279, A226145-A226150. Sequence in context: A100974 A279538 A098680 * A115931 A323344 A323341 Adjacent sequences:  A226146 A226147 A226148 * A226150 A226151 A226152 KEYWORD nonn AUTHOR Alex Ratushnyak, May 28 2013 STATUS approved

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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)