A324272 a(n) = 2*13^(2*n).

2, 338, 57122, 9653618, 1631461442, 275716983698, 46596170244962, 7874752771398578, 1330833218366359682, 224910813903914786258, 38009927549761598877602, 6423677755909710210314738, 1085601540748741025543190722, 183466660386537233316799232018, 31005865605324792430539070211042

Offset: 0

Author

Stefano Spezia, Mar 28 2019

Keywords

• nonn
• easy

Comments

x = A324271(n) and y = a(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 A324271(0) = 181 and a(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 (169).

Crossrefs

Cf. A324271: 181*13^(13*n); A000290: n^2; A001022: 13^n; A005843: 2*n.

Programs

GAP

List([0..20], n->2*169^n);

Magma

[2*169^n: n in [0..20]];

Maple

a:=n->2*169^n: seq(a(n), n=0..20);

Mathematica

2 169^Range[0, 20]

PARI

a(n) = 2*169^n;

Formula

O.g.f.: 2/(1 - 169*x).

E.g.f.: 2*exp(169*x).

a(n) = 169*a(n-1) for n > 0.

a(n) = 2*169^n.

a(n) = A005843(A000290(A001022(n))).