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.
%I A324270 #11 Sep 08 2022 08:46:24 %S A324270 13,10706059,8816899947037,7261096233082692091, %T A324270 5979824975081619492698413,4924642999453642161875329137259, %U A324270 4055655269699050826917294183685688637,3340006507773765415151949203915063077180891,2750638979431530091290481703239822791770782516813,2265269477037980585971637173331233381403285546243728459 %N A324270 a(n) = 13*7^(7*n). %C A324270 x = a(n) and y = A324266(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(14*n+3) = 4*y^7 (see Theorem 2.1 in Chakraborty, Hoque and Sharma). %H A324270 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 A324270 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (823543). %F A324270 O.g.f.: 13/(1 - 823543*x). %F A324270 E.g.f.: 13*exp(823543*x). %F A324270 a(n) = 823543*a(n-1) for n > 0. %F A324270 a(n) = 13*823543^n. %F A324270 a(n) = A008595(A001015((A000420(n)))). %e A324270 For a(0) = 13 and A324266(0) = 2, 13^2 + 7^3 = 512 = 4*2^7. %p A324270 a:=n->13*823543^n: seq(a(n), n=0..20); %t A324270 13 823543^Range[0, 20] %o A324270 (GAP) List([0..20], n->13*823543^n); %o A324270 (Magma) [13*823543^n: n in [0..20]]; %o A324270 (PARI) a(n) = 13*823543^n; %Y A324270 Cf. A324266 (2*49^n), A001015 (seventh powers), A000420 (powers of 7), A008595 (multiples of 13). %K A324270 nonn,easy %O A324270 0,1 %A A324270 _Stefano Spezia_, Mar 22 2019