Search: id:A002523
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%I A002523
%S A002523 1,2,17,82,257,626,1297,2402,4097,6562,10001,14642,20737,
%T A002523 28562,38417,50626,65537,83522,104977,130322,160001,194482,
%U A002523 234257,279842,331777,390626,456977,531442,614657,707282
%N A002523 n^4 + 1.
%C A002523 Let Phi_k(x) be the k-th cyclotomic polynomial and form the sequence 
               Phi_k(0), Phi_k(1), Phi_k(2), ... This gives A000027 (k=2), A002061 
               (k=3), A002522 (k=4), A053699 (k=5), A002061 (k=6), A053716 (k=7), 
               A002523 (k=8), A060883 (k=9), A060884 (k=10), A060885 (k=11), A060886 
               (k=12), A060887 (k=13), A060888 (k=14), A060889 (k=15), A060890 (k=16), 
               A060891 (k=18), A060892 (k=20), A060893 (k=24), A060894 (k=30), A060895 
               (k=32), A060896 (k=36).
%C A002523 All odd prime factors of a(n) are congruent to 1 modulo 8. - Nick Hobson 
               Jan 14 2007
%C A002523 Lee and Murty, p. 685: "In spite of these remarkable advances, we are 
               still unable to determine if n^4 + 1 is infinitely often a squarefree 
               number". - Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 18 2007
%D A002523 Jung-Jo Lee and M. Ram Murty, "Dirichlet series and hyperelliptic curves", 
               Forum Math. 19(2007), 677-705.
%D A002523 Mabkhout, M. (1993). "Minoration de P(x4+1)". Rend. Sem. Fac. Sci. Univ. 
               Cagliari 63 (2): 135-148.
%H A002523 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A002523 O.g.f.: -(1-3*x+17*x^2+7*x^3+2*x^4)/(-1+x)^5 . a(n) = 5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+a(n-5) 
               - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2008
%p A002523 with (combinat):seq(fibonacci(3,n^2), n=0..29); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 21 2008
%Y A002523 Cf. A005117.
%Y A002523 Sequence in context: A155715 A054568 A060352 this_sequence A079889 A053786 
               A081744
%Y A002523 Adjacent sequences: A002520 A002521 A002522 this_sequence A002524 A002525 
               A002526
%K A002523 nonn
%O A002523 0,2
%A A002523 N. J. A. Sloane (njas(AT)research.att.com).

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