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 A226146 Numbers n such that n^2 is an average of three successive primes. 2
 49, 161, 219, 351, 363, 469, 575, 597, 671, 877, 909, 933, 1013, 1225, 1231, 1303, 1359, 1381, 1419, 1489, 1577, 1653, 1797, 1815, 1989, 2083, 2117, 2177, 2241, 2289, 2301, 2403, 2483, 2493, 2517, 2611, 2617, 2653, 2727, 2779, 2869, 2931, 3029, 3051, 3261, 3515, 3617 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..47. MATHEMATICA Select[Sqrt[Mean[#]]&/@Partition[Prime[Range[10^6]], 3, 1], IntegerQ] (* Harvey P. Dale, Oct 23 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, ", r); } p2 = p1, p1 = i; } return 0; } CROSSREFS Cf. A076304, A206279, A226145-A226150. Sequence in context: A044762 A159247 A265423 * A339730 A338011 A066551 Adjacent sequences: A226143 A226144 A226145 * A226147 A226148 A226149 KEYWORD nonn AUTHOR Alex Ratushnyak, May 28 2013 STATUS approved

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Last modified June 4 13:02 EDT 2023. Contains 363128 sequences. (Running on oeis4.)