A324267 a(n) = 11*7^(5*n).

11, 184877, 3107227739, 52223176609373, 877714929273732011, 14751754816303613908877, 247932743197614838966495739, 4167005614922312598509893885373, 70034863369999307843155786531464011, 1177075948659578366919919304234315632877, 19783115469121533612823083746266142841763739

Offset: 0

Author

Stefano Spezia, Feb 26 2019

Keywords

• nonn
• easy

Comments

x = a(n) and y = A324266(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(10*n+1) = 4*y^5 (see Theorem 2.1 in Chakraborty, Hoque and Sharma).

Examples

			For a(0) = 11 and A324266(0) = 2, 11^2 + 7 = 128 = 4*2^5.
		

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 (16807).

Crossrefs

Cf. A324266: 2*49^n; A000290: n^2; A000584: n^5; A109808: 2*7^(n-1).

Programs

GAP

List([0..20], n->11*16807*n);

Magma

[11*16807^n: n in [0..20]];

Maple

a:=n->11*16807^n: seq(a(n), n=0..20);

Mathematica

11*16807^Range[0,20]

PARI

a(n) = 11*16807^n;

Formula

a(n) = 11*16807^n.

O.g.f.: 11/(1 - 16807*x).

E.g.f.: 11*exp(16807*x).

a(n) = 16807*a(n-1) for n > 0.

a(n) = 11*((7/2)*A109808(n))^5.