A146509 Numbers that are congruent to {1, 5} mod 18.

1, 5, 19, 23, 37, 41, 55, 59, 73, 77, 91, 95, 109, 113, 127, 131, 145, 149, 163, 167, 181, 185, 199, 203, 217, 221, 235, 239, 253, 257, 271, 275, 289, 293, 307, 311, 325, 329, 343, 347, 361, 365, 379, 383, 397, 401, 415, 419, 433, 437, 451, 455, 469, 473, 487

Offset

1,2

Comments

Positive integers k such that Hypergeometric[k/6,(6-k)/6,1/2,3/4] = 2Cos[2Pi/9].

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

a(2k-1) = 18*(k-1)+1, a(2k) = 18*(k-1)+5, where k>0.

G.f.: x*(1+4*x+13*x^2)/((1+x)*(1-x)^2). - Vincenzo Librandi, Jul 11 2012

a(n) = (18*n - 5*(-1)^n - 21)/2. - Bruno Berselli, Jul 12 2012 [Corrected by David Lovler, Sep 24 2022

a(1)=1, a(n) = 18*n -a(n-1) -30. - Vincenzo Librandi, Jul 12 2012

E.g.f.: 13 + ((18*x - 21)*exp(x) - 5*exp(-x))/2. - David Lovler, Sep 05 2022

Mathematica

Select[Range[500], MemberQ[{1, 5}, Mod[#, 18]]&] (* Harvey P. Dale, Jul 24 2011 *)

Prog

(Magma) [n: n in [1..500] | n mod 18 in [1, 5]]; // Bruno Berselli, Jul 12 2012
(PARI) a(n)=n\2*18+if(n%2, 1, -13) \\ Charles R Greathouse IV, Jul 14 2012

Crossrefs

Cf. A146507, A146511, A146512.

Sequence in context: A097934 A191609 A191084 * A062340 A167766 A106957

Adjacent sequences: A146506 A146507 A146508 * A146510 A146511 A146512

Keyword

nonn,easy

Author

Artur Jasinski, Oct 30 2008

Extensions

Crossrefs corrected by Ray Chandler, Dec 06 2016

Status

approved