A168671 Numbers that are congruent to {1, 10} mod 13.

1, 10, 14, 23, 27, 36, 40, 49, 53, 62, 66, 75, 79, 88, 92, 101, 105, 114, 118, 127, 131, 140, 144, 153, 157, 166, 170, 179, 183, 192, 196, 205, 209, 218, 222, 231, 235, 244, 248, 257, 261, 270, 274, 283, 287, 296, 300, 309, 313, 322, 326, 335, 339, 348, 352, 361, 365, 374

Offset

1,2

Comments

Conjecture: For no n>1 in the sequence 36*n^2+72*n+35 is equal to p*(p+2), where p, p+2 are twin primes.

The conjecture is evident, it can be proved as in A169599. [Bruno Berselli, Jan 07 2013]

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

From Vincenzo Librandi, Jul 11 2012, modified Jul 07 2015: (Start)

G.f.: x*(1+9*x+3*x^2)/((1+x)*(1-x)^2).

a(n) = (26*n+5*(-1)^n-17)/4.

a(n) = a(n-2) +13 = a(n-1) +a(n-2) -a(n-3). (End)

Mathematica

Select[Range[374], MemberQ[{1, 10}, Mod[#, 13]]&] (* Ray Chandler, Jul 08 2015 *)
LinearRecurrence[{1, 1, -1}, {1, 10, 14}, 58] (* Ray Chandler, Jul 08 2015 *)
Rest[CoefficientList[Series[x*(1+9*x+3*x^2)/((1+x)*(1-x)^2), {x, 0, 58}], x]] (* Ray Chandler, Jul 08 2015 *)

Crossrefs

Sequence in context: A084278 A286843 A069207 * A136197 A071620 A175664

Adjacent sequences: A168668 A168669 A168670 * A168672 A168673 A168674

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 02 2009

Extensions

4 leading terms added. Conjecture clarified. - R. J. Mathar, Jul 07 2015

Status

approved