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

%I A206546 #33 Aug 31 2019 19:19:14
%S A206546 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,
%T A206546 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,
%U A206546 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
%N A206546 Period 8: repeat [1, 7, 11, 13, 13, 11, 7, 1].
%C A206546 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.
%H A206546 Antti Karttunen, <a href="/A206546/b206546.txt">Table of n, a(n) for n = 1..8192</a>
%H A206546 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,-1,1,-1,1).
%F A206546 a(n) = A007775(n) (Modd 15) := Modd15(A007775(n)), n>=1, with the periodic sequence Modd15 (period length 30) given in the comment section.
%F A206546 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).
%F A206546 a(n) = -k^2 + 7k + 1 where k = (n-1) mod 8. - _David A. Corneth_, Aug 13 2017
%e A206546 Residues Modd 15 of the positive odd numbers relatively prime to 15:
%e A206546 A007775: 1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, ...
%e A206546 Modd 15: 1, 7, 11, 13, 13, 11,  7,  1,  1,  7, 11, 13, 13, 11, ...
%t A206546 PadRight[{},100,{1,7,11,13,13,11,7,1}] (* _Harvey P. Dale_, Sep 30 2015 *)
%o A206546 (PARI) a(n)=[1, 7, 11, 13, 13, 11, 7, 1][n%8+1] \\ _Charles R Greathouse IV_, Jul 17 2016
%o A206546 (Scheme) (define (A206546 n) (list-ref '(1 7 11 13 13 11 7 1) (modulo (- n 1) 8))) ;; _Antti Karttunen_, Aug 10 2017
%Y A206546 Cf. A007775, A010877.
%Y A206546 Cf. A206545 and further crossrefs given there.
%K A206546 nonn,easy
%O A206546 1,2
%A A206546 _Wolfdieter Lang_, Feb 10 2012