

A098562


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


10



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
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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: A215685 A262810 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 bfile corrected by Andrew Howroyd, Feb 28 2018


STATUS

approved



