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

Author

Wolfdieter Lang, Feb 09 2012

Keywords

• nonn
• easy

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.

Examples

			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, ...
		

Links

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

Crossrefs

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

Programs

Mathematica

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

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

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).