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.

A324272 a(n) = 2*13^(2*n).

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%I A324272 #7 Sep 08 2022 08:46:24
%S A324272 2,338,57122,9653618,1631461442,275716983698,46596170244962,
%T A324272 7874752771398578,1330833218366359682,224910813903914786258,
%U A324272 38009927549761598877602,6423677755909710210314738,1085601540748741025543190722,183466660386537233316799232018,31005865605324792430539070211042
%N A324272 a(n) = 2*13^(2*n).
%C A324272 x = A324271(n) and y = a(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(26*n+1) = 4*y^13 (see Theorem 2.1 in Chakraborty, Hoque and Sharma).
%H A324272 K. Chakraborty, A. Hoque, R. Sharma, <a href="https://arxiv.org/abs/1812.11874">Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations</a>, arXiv:1812.11874 [math.NT], 2018.
%H A324272 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (169).
%F A324272 O.g.f.: 2/(1 - 169*x).
%F A324272 E.g.f.: 2*exp(169*x).
%F A324272 a(n) = 169*a(n-1) for n > 0.
%F A324272 a(n) = 2*169^n.
%F A324272 a(n) = A005843(A000290(A001022(n))).
%e A324272 For A324271(0) = 181 and a(0) = 2, 181^2 + 7 = 32768 = 4*2^13.
%p A324272 a:=n->2*169^n: seq(a(n), n=0..20);
%t A324272 2 169^Range[0, 20]
%o A324272 (GAP) List([0..20], n->2*169^n);
%o A324272 (Magma) [2*169^n: n in [0..20]];
%o A324272 (PARI) a(n) = 2*169^n;
%Y A324272 Cf. A324271: 181*13^(13*n); A000290: n^2; A001022: 13^n; A005843: 2*n.
%K A324272 nonn,easy
%O A324272 0,1
%A A324272 _Stefano Spezia_, Mar 28 2019