A324271 - OEIS

%I #9 Sep 08 2022 08:46:24

%S 181,54820394293197793,16603732764981619615170330497629,

%T 5028857331023091670255052219467889871886268137,

%U 1523115700170851818946635098990437850680396062232555484942661,461313830041580805547042416276650834293620917849684448198307537920811805233,139720475446324270671242216643939258928764157180440338773843068067157129372210783782659949

%N a(n) = 181*13^(13*n).

%C x = a(n) and y = A324272(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 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 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (302875106592253).

%F O.g.f.: 181/(1 - 302875106592253*x).

%F E.g.f.: 181*exp(302875106592253*x).

%F a(n) = 302875106592253*a(n-1) for n > 0.

%F a(n) = 181*302875106592253^n.

%F a(n) = 181*A010801(A001022(n)).

%e For a(0) = 181 and A324272(0) = 2, 181^2 + 7 = 32768 = 4*2^13.

%p a:=n->181*302875106592253^n: seq(a(n), n=0..20);

%t 181 302875106592253^Range[0, 20]

%o (GAP) List([0..20], n->181*302875106592253^n);

%o (Magma) [181*302875106592253^n: n in [0..20]];

%o (PARI) a(n) = 181*302875106592253^n;

%Y Cf. A324272: 2*13^(2*n); A010801: n^13; A001022: 13^n.

%K nonn,easy

%O 0,1

%A _Stefano Spezia_, Mar 28 2019