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

1,2

Comments

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

Links

Table of n, a(n) for n=1..53.

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

Mathematica

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

Crossrefs

Sequence in context: A042401 A042402 A247394 * A081644 A256619 A055109

Adjacent sequences: A056078 A056079 A056080 * A056082 A056083 A056084

Keyword

nonn,easy

Author

Robert G. Wilson v, Jun 08 2000

Extensions

Definition rewritten by Bruno Berselli, Nov 19 2012

Status

approved