A178248 a(n) = 12^n + 1.

2, 13, 145, 1729, 20737, 248833, 2985985, 35831809, 429981697, 5159780353, 61917364225, 743008370689, 8916100448257, 106993205379073, 1283918464548865, 15407021574586369, 184884258895036417, 2218611106740436993

Offset: 0

Author

Stuart Clary, Dec 20 2010

Keywords

• nonn
• easy

Comments

Prime factors of a(n) are in the Cunningham Project.

Examples

			a(3) = 12^3 + 1 = 1729.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• S. S. Wagstaff, Jr., The Cunningham Project.
• Index entries for linear recurrences with constant coefficients, signature (13,-12).

Crossrefs

Cf. A000051, A001021, A007689, A016125, A024140, A034472, A034474, A034491, A034524, A052539, A062394, A062395, A062396, A062397, A063376, A063481, A074600-A074624, A228081.

Programs

Magma

[12^n + 1: n in [0..20]]; // Vincenzo Librandi, May 02 2011

Mathematica

nmax = 17; 12^Range[0, nmax] + 1
LinearRecurrence[{13,-12},{2,13},20] (* Harvey P. Dale, Nov 02 2015 *)

PARI

vector(21,n,12^(n-1)+1) \\ Charles R Greathouse IV, May 02 2011

Formula

O.g.f.: (2-13*x)/(1-13*x+12*x^2) = (2-13*x)/((1-x)(1-12*x)).

E.g.f.: exp(x) + exp(12*x). - Stefano Spezia, Mar 20 2023

From Elmo R. Oliveira, Dec 15 2023: (Start)

a(n) = 12*a(n-1) - 11 for n>0.

a(n) = 13*a(n-1) - 12*a(n-2) for n>1.

a(n) = A001021(n)+1 = A024140(n)+2.

a(n) = (11*A016125(n) + 13)/12. (End)