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 A324265 #18 Sep 08 2022 08:46:24 %S A324265 5,1715,588245,201768035,69206436005,23737807549715,8142067989552245, %T A324265 2792729320416420035,957906156902832072005,328561811817671400697715, %U A324265 112696701453461290439316245,38654968598537222620685472035,13258654229298267358895116908005,4547718400649305704101025099445715 %N A324265 a(n) = 5*343^n. %C A324265 x = a(n) and y = A324266(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(6*n+1) = 4*y^3 (see Theorem 2.1 in Chakraborty, Hoque and Sharma). %H A324265 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. %F A324265 O.g.f.: 5/(1 - 343*x). %F A324265 E.g.f.: 5*exp(343*x). %F A324265 a(n) = 343*a(n-1) for n > 0. %F A324265 a(n) = (1/25)*(A193577(n))^3. %e A324265 For a(0) = 5 and A324266(0) = 2, 5^2 + 7 = 32 = 4*2^3. %p A324265 a:=n->5*343^n: seq(a(n), n=0..20); %t A324265 5*343^Range[0,20] %o A324265 (GAP) List([0..20], n->5*343^n); %o A324265 (Magma) [5*343^n: n in [0..20]]; %o A324265 (PARI) a(n) = 5*343^n; %Y A324265 Cf. A324266 (2*49^n), A000290 (n^2), A000578 (n^3), A193577 (5*7^n). %K A324265 nonn,easy %O A324265 0,1 %A A324265 _Stefano Spezia_, Feb 20 2019