A324268 a(n) = 31*11^(5*n).

31, 4992581, 804060162631, 129494693251885181, 20855249842909360285231, 3358758842450395383296737781, 540931470335478626875322916367831, 87117554228999168336897631003955550381, 14030369226134545059825700370818045344410431, 2259604994238194616429988870420617020762644322981

Offset

0,1

Comments

x = a(n) and y = A324269(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 11^(10*n+1) = 4*y^5 (see Theorem 2.1 in Chakraborty, Hoque and Sharma).

Links

Table of n, a(n) for n=0..9.

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 (161051).

Formula

O.g.f.: 31/(1 - 161051*x).

E.g.f.: 31*exp(161051*x).

a(n) = 161051*a(n-1) for n > 0.

a(n) = 31*161051^n.

a(n) = 31*A001020(n)^5.

Example

For a(0) = 31 and A324269(0) = 3, 31^2 + 11 = 972 = 4*3^5.

Maple

a:=n->31*161051^n: seq(a(n), n=0..20);

Mathematica

31 161051^Range[0, 20]

Prog

(GAP) List([0..20], n->31*161051^n);
(Magma) [31*161052^n: n in [0..20]];
(PARI) a(n) = 31*161051^n;

Crossrefs

Cf. A324269: 3*11^(2*n); A000290: n^2; A000584: n^5; A001020: 11^n.

Sequence in context: A051155 A342118 A216791 * A145210 A091308 A023927

Adjacent sequences: A324265 A324266 A324267 * A324269 A324270 A324271

Keyword

nonn,easy

Author

Stefano Spezia, Feb 26 2019

Status

approved