A109796 a(n) = prime(1^4) + prime(2^4) + ... + prime(n^4).

2, 55, 474, 2093, 6730, 17357, 38748, 77621, 143308, 248037, 407558, 641437, 973380, 1432721, 2052922, 2874563, 3944166, 5314265, 7045924, 9206477, 11874460, 15134597, 19083406, 23826383, 29480190, 36172177, 44039724

Offset: 1

Author

Jonathan Vos Post, Aug 15 2005

Keywords

• nonn

Comments

Analog of prime(1^2) + prime(2^2) + ... + prime(n^2) (A109724). For a(n) to be prime for n > 1 it is necessary but not sufficient that n == 0 (mod 4).

Examples

			a(1) = 2 because prime(1^4) = prime(1) = 2.
a(2) = 55 because prime(1^4) + prime(2^4) = prime(1) + prime(16) = 2 + 53.
a(3) = 474 because prime(1^4) + prime(2^4) + prime(3^4) = prime(1) + prime(16) + prime(81) = 2 + 53 + 419.
a(4) = 2093 because prime(1^4) + prime(2^4) + prime(3^4) + prime(4^4) = 2 + 53 + 419 + prime(256) = 2 + 53 + 419 + 1619.
a(8) = 2 + 53 + 419 + 1619 + 4637 + 10627 + 21391 + 38873 = 77621 (which is prime).
a(12) = 2 + 53 + 419 + 1619 + 4637 + 10627 + 21391 + 38873 + 65687 + 104729 + 159521 + 233879 = 641437 (which is prime).
a(28) = 2 + 53 + 419 + 1619 + 4637 + 10627 + 21391 + 38873 + 65687 + 104729 + 159521 + 233879 + 331943 + 459341 + 620201 + 821641 + 1069603 + 1370099 + 1731659 + 2160553 + 2667983 + 3260137 + 3948809 + 4742977 + 5653807 + 6691987 + 7867547 + 9195889 = 53235613 (which is prime).
It is a coincidence that a(1), a(2) and a(3) are all palindromes.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..100
• Eric Weisstein's World of Mathematics, Biquadratic Number.

Crossrefs

First differences are A109791.

Cf. A000040, A000290, A000583, A011757, A109724, A109770.

Programs

Mathematica

Accumulate[Table[Prime[n^4],{n,30}]] (* Harvey P. Dale, Feb 02 2019 *)

PARI

A109796(n)={
        sum(i=1,n,prime(i^4))
} /* R. J. Mathar, Mar 09 2012 */

Formula

a(n) = Sum_{i=1..n} A000040(A000583(i)).