A166639 a(n) = 6*n + 3 + 4*(-1)^n.

7, 5, 19, 17, 31, 29, 43, 41, 55, 53, 67, 65, 79, 77, 91, 89, 103, 101, 115, 113, 127, 125, 139, 137, 151, 149, 163, 161, 175, 173, 187, 185, 199, 197, 211, 209, 223, 221, 235, 233, 247, 245, 259, 257, 271, 269, 283, 281, 295, 293, 307, 305, 319, 317, 331, 329

Offset

0,1

Comments

Prime pairs in this sequence of form p, p+14 (5,19 - 17,31 - 29,43 - 53,67 - 89,103 - 113,127 - 137,151 - 149,163 - 197,211 - 257, 271 - 269,283 and so on).

The numerators in the continued fraction of 2^(7/12) = 1 + 7/(12 + 5/(2 + 19/(36 + 17/(2 + 31/(60 + 29/(2 + 43/(84 + 41/(2 + ...)))))))). - Philippe Deléham, Nov 02 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (7-2*x+7*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Feb 07 2011

From G. C. Greubel, May 20 2016: (Start)

E.g.f.: (6*x + 7)*cosh(x) + (6*x - 1)*sinh(x).

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

Sum_{n>=0} (-1)^(n+1)/a(n) = (1/6 - 1/(4*sqrt(3)))*Pi. - Amiram Eldar, Feb 25 2023

Mathematica

Table[(6 n + 3 + 4*(-1)^n), {n, 0, 80}] (* Vincenzo Librandi, Sep 15 2013 *)
LinearRecurrence[{1, 1, -1}, {7, 5, 19}, 50] (* G. C. Greubel, May 20 2016 *)

Prog

(Magma) [6*n+3+4*(-1)^n: n in [0..60]]; // Vincenzo Librandi, Sep 15 2013

Crossrefs

Sequence in context: A284085 A204138 A179118 * A078747 A213835 A145396

Adjacent sequences: A166636 A166637 A166638 * A166640 A166641 A166642

Keyword

nonn,easy

Author

Vincenzo Librandi, Oct 18 2009

Extensions

Corrected sign on the recommendation of Zak Seidov

Changed offset from 1 to 0 and added a(0) by Vincenzo Librandi, Sep 15 2013

Adapted G.f. to new offset by Vincenzo Librandi, Sep 15 2013

Status

approved