A206545 Period length 16: repeat 1, 3, 5, 7, 9, 11, 13, 15, 15, 13, 11, 9, 7, 5, 3, 1.

1, 3, 5, 7, 9, 11, 13, 15, 15, 13, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 13, 15, 15, 13, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 13, 15, 15, 13, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 13, 15, 15, 13, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 13, 15, 15, 13, 11, 9, 7, 5, 3, 1

Offset

1,2

Comments

For general Modd n see a comment on A203571. This sequence gives the Modd 17 residues of the odd numbers not divisible by 17, which are given in A204458.

The underlying periodic sequence with period length 34 is periodic (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 4, 3, 2, 1). This sequence with offset 0 is called P_17 or Modd17.

Links

Table of n, a(n) for n=1..80.

Formula

a(n) = A204458(n) (Modd 17) := Modd17(A204458(n)), n>=1, with the periodic sequence Modd17, with period length 34, defined in the comment section.

O.g.f.: x*(1+x^15+3*x*(1+x^13)+5*x^2*(1+x^11)+7*x^3*(1+x^9)+9*x^4*(1+x^7)+11*x^5*(1+x^5)+ 13*x^6*(1+x^3)+15*x^7*(1+x))/(1-x^16) = x*(1+x)^2*(1+x^2)*(1+x^4)/((1+x^8)*(1-x)).

Example

Residue Modd 17 of the positive odd numbers not divisible by 17:
A204458: 1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 25, 27, 29,...
Modd 17: 1, 3, 5, 7, 9, 11, 13, 15, 15, 13, 11,  9,  7,  5,...

Mathematica

PadRight[{}, 120, Join[Range[1, 15, 2], Range[15, 1, -2]]] (* Harvey P. Dale, Sep 21 2018 *)

Crossrefs

Cf. A000012 (Modd 3), A084101 (Modd 5), A110551 (Modd 7), A206543 (Modd 11), A206544 (Modd 13).

Sequence in context: A187411 A189401 A091569 * A293703 A120890 A321499

Adjacent sequences: A206542 A206543 A206544 * A206546 A206547 A206548

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 09 2012

Status

approved