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A109796
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a(n) = prime(1^4) + prime(2^4) + ... + prime(n^4).
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1
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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
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..100
Eric Weisstein's World of Mathematics, "Biquadratic Number."
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FORMULA
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a(n) = Sum_{i=1..n} A000040(A000583(i)).
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EXAMPLE
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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.
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MATHEMATICA
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Accumulate[Table[Prime[n^4], {n, 30}]] (* Harvey P. Dale, Feb 02 2019 *)
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PROG
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(PARI) A109796(n)={
sum(i=1, n, prime(i^4))
} /* R. J. Mathar, Mar 09 2012 */
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CROSSREFS
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First differences are A109791.
Cf. A000040, A000290, A000583, A011757, A109724, A109770.
Sequence in context: A280209 A157262 A007975 * A186886 A024029 A134501
Adjacent sequences: A109793 A109794 A109795 * A109797 A109798 A109799
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post, Aug 15 2005
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STATUS
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approved
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