A206546 Period 8: repeat [1, 7, 11, 13, 13, 11, 7, 1].

1, 7, 11, 13, 13, 11, 7, 1, 1, 7, 11, 13, 13, 11, 7, 1, 1, 7, 11, 13, 13, 11, 7, 1, 1, 7, 11, 13, 13, 11, 7, 1, 1, 7, 11, 13, 13, 11, 7, 1, 1, 7, 11, 13, 13, 11, 7, 1, 1, 7, 11, 13, 13, 11, 7, 1, 1, 7, 11, 13, 13, 11, 7, 1, 1, 7, 11, 13, 13, 11, 7, 1, 1, 7, 11, 13, 13, 11, 7, 1, 1, 7, 11, 13, 13, 11, 7, 1, 1, 7, 11, 13, 13, 11, 7, 1

Offset: 1

Author

Wolfdieter Lang, Feb 10 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 15 of the positive odd numbers relatively prime to 15 (the positive odd numbers from all reduced residue classes mod 15), shown in A007775. The underlying periodic sequence with period length 30 is [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,0,14,13,12,11,10,9,8,7,6,5,4,3,2,1], called, with offset 0, P_15 or Modd15.

Examples

			Residues Modd 15 of the positive odd numbers relatively prime to 15:
A007775: 1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, ...
Modd 15: 1, 7, 11, 13, 13, 11,  7,  1,  1,  7, 11, 13, 13, 11, ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1,-1,1).

Crossrefs

Cf. A007775, A010877.

Cf. A206545 and further crossrefs given there.

Programs

Mathematica

PadRight[{},100,{1,7,11,13,13,11,7,1}] (* Harvey P. Dale, Sep 30 2015 *)

PARI

a(n)=[1, 7, 11, 13, 13, 11, 7, 1][n%8+1] \\ Charles R Greathouse IV, Jul 17 2016

Scheme

(define (A206546 n) (list-ref '(1 7 11 13 13 11 7 1) (modulo (- n 1) 8))) ;; Antti Karttunen, Aug 10 2017

Formula

a(n) = A007775(n) (Modd 15) := Modd15(A007775(n)), n>=1, with the periodic sequence Modd15 (period length 30) given in the comment section.

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

a(n) = -k^2 + 7k + 1 where k = (n-1) mod 8. - David A. Corneth, Aug 13 2017