Search: id:A109796
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%I A109796
%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 Prime[1^4] + prime[2^4] + ... + prime[n^4].
%C A109796 Analogue 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).
%H A109796 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               BiquadraticNumber.html">"Biquadratic Number."</a>
%F A109796 Sum of A000040(A000583(i)) from i = 1 to n.
%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(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(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(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.
%Y A109796 Cf. A000040, A000290, A000583, A011757, A109724, A109770.
%Y A109796 Sequence in context: A034013 A157262 A007975 this_sequence A024029 A134501 
               A037176
%Y A109796 Adjacent sequences: A109793 A109794 A109795 this_sequence A109797 A109798 
               A109799
%K A109796 nonn
%O A109796 1,1
%A A109796 Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 15 2005

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