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

%I A109796 #23 Feb 16 2025 08:32:58
%S A109796 2,55,474,2093,6730,17357,38748,77621,143308,248037,407558,641437,
%T A109796 973380,1432721,2052922,2874563,3944166,5314265,7045924,9206477,
%U A109796 11874460,15134597,19083406,23826383,29480190,36172177,44039724
%N A109796 a(n) = prime(1^4) + prime(2^4) + ... + prime(n^4).
%C A109796 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).
%H A109796 Harvey P. Dale, <a href="/A109796/b109796.txt">Table of n, a(n) for n = 1..100</a>
%H A109796 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number</a>.
%F A109796 a(n) = Sum_{i=1..n} A000040(A000583(i)).
%e A109796 a(1) = 2 because prime(1^4) = prime(1) = 2.
%e A109796 a(2) = 55 because prime(1^4) + prime(2^4) = prime(1) + prime(16) = 2 + 53.
%e A109796 a(3) = 474 because prime(1^4) + prime(2^4) + prime(3^4) = prime(1) + prime(16) + prime(81) = 2 + 53 + 419.
%e A109796 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.
%e A109796 a(8) = 2 + 53 + 419 + 1619 + 4637 + 10627 + 21391 + 38873 = 77621 (which is prime).
%e A109796 a(12) = 2 + 53 + 419 + 1619 + 4637 + 10627 + 21391 + 38873 + 65687 + 104729 + 159521 + 233879 = 641437 (which is prime).
%e A109796 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).
%e A109796 It is a coincidence that a(1), a(2) and a(3) are all palindromes.
%t A109796 Accumulate[Table[Prime[n^4],{n,30}]] (* _Harvey P. Dale_, Feb 02 2019 *)
%o A109796 (PARI) A109796(n)={
%o A109796         sum(i=1,n,prime(i^4))
%o A109796 } /* _R. J. Mathar_, Mar 09 2012 */
%Y A109796 First differences are A109791.
%Y A109796 Cf. A000040, A000290, A000583, A011757, A109724, A109770.
%K A109796 nonn
%O A109796 1,1
%A A109796 _Jonathan Vos Post_, Aug 15 2005