A122211 Numbers k such that the sum of squares of the first k^2 primes is a prime.

6, 12, 30, 66, 156, 180, 228, 336, 366, 558, 750, 840, 894, 978, 1398, 1410, 1506, 1560, 1578, 1662, 1794, 1800, 1812, 1824, 1890, 1992, 2094, 2268, 2334, 2358, 2430, 2604, 2736, 2742, 2766, 2802, 2856, 2922, 3042, 3312, 3390, 3702, 3948, 3954, 3984, 4170, 4314

Offset: 1

Author

Alexander Adamchuk, Aug 26 2006

Keywords

• nonn

Comments

Corresponding primes A122209(a(n)) = A024450(a(n)^2) are listed in A122210(n) = {239087, 29194283, 13459558559, 2330212120559, ...}. All a(n) are of the form 6*m, where m = {1, 2, 5, 11, 26, 30, 38, 56, 61, 93, 125, 140, 149, 163, 233, 235, 251, 260, 263, 277, 299, 300, ...}. Because A122209(2*m-1) is an even number and A122209(3*m-1) == A122209(3*m+1) == 0 (mod 3) for m >= 1. [Edited by Jinyuan Wang, Mar 23 2020]

Crossrefs

Cf. A024450, A098561, A098562, A122209, A122210.

Programs

Mathematica

s=0;Do[p=Prime[n];k=Sqrt[n];s=s+p*p;If[PrimeQ[s]&&IntegerQ[k],Print[{k,n,s}]],{n,1,10^7}]

Formula

A122209(a(n)) = A024450(a(n)^2) = A122210(n).

Extensions

More terms from Jinyuan Wang, Mar 23 2020