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

Author

Artur Jasinski, Oct 30 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A146507, A146511, A146512.

Programs

Magma

[n: n in [1..500] | n mod 18 in [1,5]]; // Bruno Berselli, Jul 12 2012

Mathematica

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

PARI

a(n)=n\2*18+if(n%2,1,-13) \\ Charles R Greathouse IV, Jul 14 2012

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

Extensions

Crossrefs corrected by Ray Chandler, Dec 06 2016