A056081 Numbers that are congruent to {1, 26} mod 27.

1, 26, 28, 53, 55, 80, 82, 107, 109, 134, 136, 161, 163, 188, 190, 215, 217, 242, 244, 269, 271, 296, 298, 323, 325, 350, 352, 377, 379, 404, 406, 431, 433, 458, 460, 485, 487, 512, 514, 539, 541, 566, 568, 593, 595, 620, 622, 647, 649, 674, 676, 701, 703

Offset: 1

Author

Robert G. Wilson v, Jun 08 2000

Keywords

• nonn
• easy

Comments

Numbers k such that k^2 == 1 (mod 3^3).

Links

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

Programs

Mathematica

x=3; Select[ Range[ 1000 ], PowerMod[ #, x-1, x^3 ]==1& ]

Formula

a(n) = 27*(n-1)-a(n-1) with n>1, a(1) = 1. - Vincenzo Librandi, Aug 07 2010

G.f.: x*(1+25*x+x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 10 2015

Sum_{n>=1} (-1)^(n+1)/a(n) = cot(Pi/27)*Pi/27. - Amiram Eldar, Dec 31 2021

Extensions

Definition rewritten by Bruno Berselli, Nov 19 2012