cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A297493 a(n) = (1/2) * Sum_{|k|<=2*sqrt(p)} k^8*H(4*p-k^2) where H() is the Hurwitz class number and p is n-th prime.

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%I A297493 #14 Jan 01 2018 12:03:05
%S A297493 129,2444,39714,224664,2214948,5133114,19734534,34465980,89757384,
%T A297493 286456170,399954528,969369474,1620023118,2055854724,3207878544,
%U A297493 5850511794,10003119540,11817917898,18893239884,25249088088,29012002734,43064859120,55130420604
%N A297493 a(n) = (1/2) * Sum_{|k|<=2*sqrt(p)} k^8*H(4*p-k^2) where H() is the Hurwitz class number and p is n-th prime.
%H A297493 Seiichi Manyama, <a href="/A297493/b297493.txt">Table of n, a(n) for n = 1..1000</a>
%H A297493 N. Lygeros, O. Rozier, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Lygeros/lygeros5.html">A new solution to the equation tau(p) == 0 (mod p)</a>, J. Int. Seq. 13 (2010) # 10.7.4.
%F A297493 Let b(n) = 14*n^5 - 28*n^3 - 20*n^2 - 7*n - 1.
%F A297493 a(n) = b(prime(n)).
%o A297493 (PARI) lista(nn) = forprime(p=2, nn, print1(14*p^5-28*p^3-20*p^2-7*p-1, ", ")); \\ _Altug Alkan_, Jan 01 2018
%Y A297493 (1/2) * Sum_{|k|<=2*sqrt(p)} k^m*H(4*p-k^2): A000040 (m=0), A084920 (m=2), A297491 (m=4), A297492 (m=6), this sequence (m=8), A297494 (m=10).
%Y A297493 Cf. A259825.
%K A297493 nonn
%O A297493 1,1
%A A297493 _Seiichi Manyama_, Dec 31 2017