A206544 Period 12: repeat 1, 3, 5, 7, 9, 11, 11, 9, 7, 5, 3, 1.

1, 3, 5, 7, 9, 11, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 11, 9, 7, 5, 3, 1

Offset

1,2

Comments

For general Modd n (not to be confused with mod n) see a comment on A203571. The present sequence gives the residues Modd 13 of the positive odd numbers not divisible by 13, which are given in A204457.

The underlying periodic sequence with period length 26 is periodic([0,1,2,3,4,5,6,7,8,9,10,11,12,0,12,11,10,9,8,7,6,5,4,3,2,1]), called, with offset 0, P_13 or Modd13.

Links

Table of n, a(n) for n=1..72.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, -1, 1).

Formula

a(n) = A204457(n) (Modd 13) := Modd13(A204457(n)), n>=1, with the period length 26 periodic sequence Modd13 given in the comment section.

O.g.f.: x*(1+x^11+3*x*(1+x^9)+5*x^2*(1+x^7)+7*x^3*(1+x^5)+9*x^4*(1+x^3)+11*x^5*(1+x))/(1-x^12) = x*(1-x^6)*(1+x)/((1+x^6)*(1-x)^2).

Example

Residue Modd 13 of the positive odd numbers not divisible by 13:
A204457: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, ...
Modd 13: 1, 3, 5, 7, 9, 11, 11,  9,  7,  5,  3,  1,  1,  3,  5,  7, ...

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, -1, 1}, {1, 3, 5, 7, 9, 11, 11}, 72] (* Ray Chandler, Aug 08 2015 *)

Prog

(PARI) a(n)=[1, 1, 3, 5, 7, 9, 11, 11, 9, 7, 5, 3][n%12+1] \\ Charles R Greathouse IV, Jul 17 2016

Crossrefs

Cf. A000012 (Modd 3), A084101 (Modd 5), A110551 (Modd 7), A206543 (Modd 11).

Sequence in context: A098160 A371215 A103701 * A122799 A345425 A362022

Adjacent sequences: A206541 A206542 A206543 * A206545 A206546 A206547

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 09 2012

Status

approved