A098562 Primes that are the sum of the squares of the first k primes for some k.

13, 20477, 75997, 239087, 2210983, 3579761, 29194283, 40002073, 45448471, 55600481, 77290091, 108095623, 114986483, 155637463, 226226771, 302920139, 324657881, 519681709, 551321299, 618359839, 797005427, 944007487, 1039681147, 1124764853, 1923614047, 2135308631

Offset

1,1

Comments

These are the primes arising in A098561.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..15000

Example

From K. D. Bajpai, Dec 15 2014: (Start)
13 is in the sequence because the sum of the squares of the first 2 primes is 2^2 + 3^2 = 4 + 9 = 13, which is prime.
20477 is in the sequence because the sum of the squares of the first 18 primes is 2^2 + 3^2 + 5^2 + ... + 59^2 + 61^2 = 4 + 9 + 25 + ... + 3481 + 3721 = 20477, which is prime.
(End)

Mathematica

Select[Table[Sum[Prime[k]^2, {k, 1, n}], {n, 1000}], PrimeQ]  (* K. D. Bajpai, Dec 15 2014 *)

Prog

(PARI)  s=0; forprime(p=2, 1e6, t=s+=p^2; if(isprime(t), print1(t, ", "))) \\ K. D. Bajpai, Dec 15 2014

Crossrefs

Cf. A098561 (corresponding n), A024450 (sum of squares of primes), A066525 (sums of cubes of primes), A013918 (sums of primes).

Cf. A000040, A006567. - Jonathan Vos Post, Aug 13 2009

Sequence in context: A262810 A340295 A203514 * A176183 A241879 A185408

Adjacent sequences: A098559 A098560 A098561 * A098563 A098564 A098565

Keyword

nonn

Author

Rick L. Shepherd, Sep 14 2004

Extensions

a(24)-a(26) from K. D. Bajpai, Dec 15 2014

a(42) in b-file corrected by Andrew Howroyd, Feb 28 2018

Status

approved