%I #38 Dec 17 2023 02:36:44

%S 2,13,145,1729,20737,248833,2985985,35831809,429981697,5159780353,

%T 61917364225,743008370689,8916100448257,106993205379073,

%U 1283918464548865,15407021574586369,184884258895036417,2218611106740436993

%N a(n) = 12^n + 1.

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

%H Vincenzo Librandi, <a href="/A178248/b178248.txt">Table of n, a(n) for n = 0..200</a>

%H S. S. Wagstaff, Jr., <a href="http://homes.cerias.purdue.edu/~ssw/cun/index.html">The Cunningham Project</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (13,-12).

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

%F E.g.f.: exp(x) + exp(12*x). - _Stefano Spezia_, Mar 20 2023

%F From _Elmo R. Oliveira_, Dec 15 2023: (Start)

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

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

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

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

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

%t nmax = 17; 12^Range[0, nmax] + 1

%t LinearRecurrence[{13,-12},{2,13},20] (* _Harvey P. Dale_, Nov 02 2015 *)

%o (Magma) [12^n + 1: n in [0..20]]; // _Vincenzo Librandi_, May 02 2011

%o (PARI) vector(21,n,12^(n-1)+1) \\ _Charles R Greathouse IV_, May 02 2011

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

%K nonn,easy

%O 0,1

%A _Stuart Clary_, Dec 20 2010