A324271 a(n) = 181*13^(13*n).

181, 54820394293197793, 16603732764981619615170330497629, 5028857331023091670255052219467889871886268137, 1523115700170851818946635098990437850680396062232555484942661, 461313830041580805547042416276650834293620917849684448198307537920811805233, 139720475446324270671242216643939258928764157180440338773843068067157129372210783782659949

Offset: 0

Author

Stefano Spezia, Mar 28 2019

Keywords

• nonn
• easy

Comments

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).

Examples

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

Links

• K. Chakraborty, A. Hoque, R. Sharma, Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations, arXiv:1812.11874 [math.NT], 2018.
• Index entries for linear recurrences with constant coefficients, signature (302875106592253).

Crossrefs

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

Programs

GAP

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

Magma

[181*302875106592253^n: n in [0..20]];

Maple

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

Mathematica

181 302875106592253^Range[0, 20]

PARI

a(n) = 181*302875106592253^n;

Formula

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

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

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

a(n) = 181*302875106592253^n.

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