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 A306472 #22 Jul 10 2025 08:13:08 %S A306472 37,999,26973,728271,19663317,530909559,14334558093,387033068511, %T A306472 10449892849797,282147106944519,7617971887502013,205685240962554351, %U A306472 5553501505988967477,149944540661702121879,4048502597865957290733,109309570142380846849791,2951358393844282864944357 %N A306472 a(n) = 37*27^n. %C A306472 x = a(n) and y = A002042(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 3^(6*n+1) = 4*y^3 (see Theorem 2.1 in Chakraborty, Hoque and Sharma). %H A306472 K. Chakraborty, A. Hoque, and 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 A306472 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (27). %F A306472 O.g.f.: 37/(1 - 27*x). %F A306472 E.g.f.: 37*exp(27*x). %F A306472 a(n) = 27*a(n-1) for n > 0. %F A306472 a(n) = 37*A009971(n). %e A306472 For a(0) = 37 and A002042(0) = 7, 37^2 + 3 = 1372 = 4*7^3. %p A306472 a:=n->37*27^n: seq(a(n), n=0..20); %t A306472 37*27^Range[0,20] %o A306472 (GAP) List([0..20], n->37*27^n); %o A306472 (Magma) [37*27^n: n in [0..20]]; %o A306472 (PARI) a(n) = 37*27^n; %Y A306472 Cf. A002042 (7*4^n), A009971 (27^n), A000290 (n^2), A000578 (n^3). %K A306472 nonn,easy %O A306472 0,1 %A A306472 _Stefano Spezia_, Feb 18 2019