A122209 -id:A122209 - cp's OEIS frontend

A122210 Primes in A122209[n].

239087, 29194283, 13459558559, 2330212120559, 591302115428891, 1475383481009147, 6659290813076243, 78234869090622611, 134532153287171039, 1936272192837757871, 12491376574210826183, 25493310333833042507

Offset: 1

Alexander Adamchuk, Aug 26 2006

nonn

Sum of squares of the first n^2 primes is A122209[n] = A024450[n^2] = {4,87,1556,13275,65796,239087,710844,1789395,4083404,8384727,16156884,29194283,...}. Corresponding numbers n such that A122209[n] is prime are listed in A122211[n] = {6,12,30,66,156,180,228,336,366,558,750,840,894,978,...}.

Cf. A122209, A122211, A024450, A098561, A098562.

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}]

a(n) = A122209[ A122211(n) ] = A024450[ A122211(n)^2 ].

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

Original entry on oeis.org

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

Alexander Adamchuk, Aug 26 2006

nonn

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]

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

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}]

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

More terms from Jinyuan Wang, Mar 23 2020

cp's OEIS Frontend

A122210 Primes in A122209[n].

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