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