A206546 -id:A206546 - cp's OEIS frontend

A206548 Period 12: repeat 1, 5, 11, 13, 17, 19, 19, 17, 13, 11, 5, 1.

1, 5, 11, 13, 17, 19, 19, 17, 13, 11, 5, 1, 1, 5, 11, 13, 17, 19, 19, 17, 13, 11, 5, 1, 1, 5, 11, 13, 17, 19, 19, 17, 13, 11, 5, 1, 1, 5, 11, 13, 17, 19, 19, 17, 13, 11, 5, 1, 1, 5, 11, 13, 17, 19, 19, 17, 13, 11, 5, 1, 1, 5, 11, 13, 17, 19, 19, 17, 13, 11, 5, 1

Offset: 1

Wolfdieter Lang, Feb 10 2012

For general Modd n (not to be confused with mod n) see a comment on A203571. The present sequence gives the residues Modd 21 of the positive odd integers relatively prime to 21 which are shown in A206547. The underlying periodic sequence with period length 42 is, with offset 0, called P_21 or also Modd21: [seq(j,j=0..20),0,seq(21-j,j=1..20)].

			Residues Modd 21 of the positive odd integers relatively prime to 21:
A206547: 1, 5, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, ...
Modd 21: 1, 5, 11, 13, 17, 19, 19, 17, 13, 11,  5,  1,  1, ...

Index entries for linear recurrences with constant coefficients, signature (2,-2,1,0,0,-1,2,-2,1).

Cf. A206546.

a(n)=[1, 1, 5, 11, 13, 17, 19, 19, 17, 13, 11, 5][n%12+1] \\ Charles R Greathouse IV, Jul 17 2016

a(n) = A206547(n) (Modd 21) := Modd21(A206547(n)), n>=1, with the periodic sequence Modd21 (period length 42) given in the comment section.
From Chai Wah Wu, Feb 16 2021: (Start)
a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) - a(n-6) + 2*a(n-7) - 2*a(n-8) + a(n-9) for n > 9.
G.f.: x*(-x^8 - 3*x^7 - 3*x^6 - 8*x^4 - 3*x^2 - 3*x - 1)/((x - 1)*(x^2 + 1)*(x^2 - x + 1)*(x^4 - x^2 + 1)). (End)

Deleted an incorrect g.f. - N. J. A. Sloane, Feb 16 2021

cp's OEIS Frontend

A206548 Period 12: repeat 1, 5, 11, 13, 17, 19, 19, 17, 13, 11, 5, 1.

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