A324270 a(n) = 13*7^(7*n).

13, 10706059, 8816899947037, 7261096233082692091, 5979824975081619492698413, 4924642999453642161875329137259, 4055655269699050826917294183685688637, 3340006507773765415151949203915063077180891, 2750638979431530091290481703239822791770782516813, 2265269477037980585971637173331233381403285546243728459

Offset: 0

Author

Stefano Spezia, Mar 22 2019

Keywords

• nonn
• easy

Comments

x = a(n) and y = A324266(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(14*n+3) = 4*y^7 (see Theorem 2.1 in Chakraborty, Hoque and Sharma).

Examples

			For a(0) = 13 and A324266(0) = 2, 13^2 + 7^3 = 512 = 4*2^7.
		

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 (823543).

Crossrefs

Cf. A324266 (2*49^n), A001015 (seventh powers), A000420 (powers of 7), A008595 (multiples of 13).

Programs

GAP

List([0..20], n->13*823543^n);

Magma

[13*823543^n: n in [0..20]];

Maple

a:=n->13*823543^n: seq(a(n), n=0..20);

Mathematica

13 823543^Range[0, 20]

PARI

a(n) = 13*823543^n;

Formula

O.g.f.: 13/(1 - 823543*x).

E.g.f.: 13*exp(823543*x).

a(n) = 823543*a(n-1) for n > 0.

a(n) = 13*823543^n.

a(n) = A008595(A001015((A000420(n)))).