A324265 a(n) = 5*343^n.

5, 1715, 588245, 201768035, 69206436005, 23737807549715, 8142067989552245, 2792729320416420035, 957906156902832072005, 328561811817671400697715, 112696701453461290439316245, 38654968598537222620685472035, 13258654229298267358895116908005, 4547718400649305704101025099445715

Offset: 0

Author

Stefano Spezia, Feb 20 2019

Keywords

• nonn
• easy

Comments

x = a(n) and y = A324266(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(6*n+1) = 4*y^3 (see Theorem 2.1 in Chakraborty, Hoque and Sharma).

Examples

			For a(0) = 5 and A324266(0) = 2, 5^2 + 7 = 32 = 4*2^3.
		

Links

• K. Chakraborty, A. Hoque, R. Sharma, Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations, arXiv:1812.11874 [math.NT], 2018.

Crossrefs

Cf. A324266 (2*49^n), A000290 (n^2), A000578 (n^3), A193577 (5*7^n).

Programs

GAP

List([0..20], n->5*343^n);

Magma

[5*343^n: n in [0..20]];

Maple

a:=n->5*343^n: seq(a(n), n=0..20);

Mathematica

5*343^Range[0,20]

PARI

a(n) = 5*343^n;

Formula

O.g.f.: 5/(1 - 343*x).

E.g.f.: 5*exp(343*x).

a(n) = 343*a(n-1) for n > 0.

a(n) = (1/25)*(A193577(n))^3.