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A109796 Prime[1^4] + prime[2^4] + ... + prime[n^4]. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 for n = 0 (mod 4).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, "Biquadratic Number."

FORMULA

Sum of A000040(A000583(i)) from i = 1 to n.

EXAMPLE

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(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(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(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.

MATHEMATICA

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

PROG

(PARI) A109796(n)={

        sum(i=1, n, prime(i^4))

} /* R. J. Mathar, Mar 09 2012 */

CROSSREFS

First differences are A109791.

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

Sequence in context: A034013 A157262 A007975 * A186886 A024029 A134501

Adjacent sequences:  A109793 A109794 A109795 * A109797 A109798 A109799

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Aug 15 2005

STATUS

approved

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Last modified November 19 22:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)