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A206548
Period 12: repeat 1, 5, 11, 13, 17, 19, 19, 17, 13, 11, 5, 1.
0
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
1,2
COMMENTS
For general Modd n (not to be confused with mod n) see a comment on A203571. The present sequence gives the residues Modd 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)].
FORMULA
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)
EXAMPLE
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, ...
PROG
(PARI) a(n)=[1, 1, 5, 11, 13, 17, 19, 19, 17, 13, 11, 5][n%12+1] \\ Charles R Greathouse IV, Jul 17 2016
CROSSREFS
Cf. A206546.
Sequence in context: A251965 A093685 A337658 * A206547 A295584 A185208
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 10 2012
EXTENSIONS
Deleted an incorrect g.f. - N. J. A. Sloane, Feb 16 2021
STATUS
approved