A206543 Period 10: repeat 1, 3, 5, 7, 9, 9, 7, 5, 3, 1.

1, 3, 5, 7, 9, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 9, 7, 5, 3, 1, 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 11 for the positive odd numbers not divisible by 11, which are given in A204454.

The underlying period length 22 sequence with offset 0 is P_11, also called Modd11, periodic([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]).

Examples

			Residue Modd 11 of the positive odd numbers not divisible by 11:
A204454: 1, 3, 5, 7, 9, 13, 15, 17, 19, 21, 23, 25, 27, ...
Modd 11: 1, 3, 5, 7, 9,  9,  7,  5,  3,  1,  1,  3,  5, ...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,1).

Crossrefs

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

Programs

Mathematica

PadRight[{},120,{1,3,5,7,9,9,7,5,3,1}] (* or *) LinearRecurrence[{2,-2,2,-2,1},{1,3,5,7,9},120] (* Harvey P. Dale, Oct 15 2017 *)

PARI

a(n)=[1, 3, 5, 7, 9, 9, 7, 5, 3, 1][n%10+1] \\ Charles R Greathouse IV, Jul 17 2016

Formula

a(n) = A204454(n) (Modd 11) := Modd11(A204454(n)), with the periodic sequence Modd11 with period length 22 given in the comment section.

O.g.f.: x*(1+x^9+3*x*(1+x^7)+5*x^2*(1+x^5)+7*x^3*(1+x^3)+9*x^4*(1+x))/(1-x^10) = x*(1+x)*(1-x^5)/((1+x^5)*(1-x)^2).