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

1,2

Comments

For general Modd n (not to be confused with mod n) see a comment on A203571. The present sequence gives the residues Modd 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]).

Links

Table of n, a(n) for n=1..61.

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

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).

Example

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, ...

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 *)

Prog

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

Crossrefs

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

Sequence in context: A252002 A139081 A196189 * A274988 A265509 A265527

Adjacent sequences: A206540 A206541 A206542 * A206544 A206545 A206546

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 09 2012

Status

approved