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A089608 a(n) = ((-1)^(n+1)*A002425(n)) modulo 6. 2

%I

%S 1,5,1,1,1,5,1,5,1,5,1,1,1,5,1,1,1,5,1,1,1,5,1,5,1,5,1,1,1,5,1,5,1,5,

%T 1,1,1,5,1,5,1,5,1,1,1,5,1,1,1,5,1,1,1,5,1,5,1,5,1,1,1,5,1,1,1,5,1,1,

%U 1,5,1,5,1,5,1,1,1,5,1,1,1,5,1,1,1,5,1,5,1,5,1,1,1,5,1,5,1,5,1,1,1,5,1,5,1

%N a(n) = ((-1)^(n+1)*A002425(n)) modulo 6.

%C Let S(1)={1} and S(n+1)=S(n)S'(n) where S'(n) is obtained from S(n) by changing last term using the cyclic permutation 1->5->1, then sequence is S(infinity).

%H Antti Karttunen, <a href="/A089608/b089608.txt">Table of n, a(n) for n = 1..65536</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

%F a(n) = 5 - 4*A035263(n).

%o (PARI) a(n)=numerator(2/n*(4^n-1)*bernfrac(2*n))%6

%o (PARI) a(n)=valuation(n,2)%2 * 4 + 1; \\ _Andrew Howroyd_, Aug 01 2018

%o (Scheme)

%o (define (A035263 n) (let loop ((n n) (i 1)) (cond ((odd? n) (modulo i 2)) (else (loop (/ n 2) (+ 1 i))))))

%o (define (A089608 n) (- 5 (* 4 (A035263 n))))

%o ;; _Antti Karttunen_, Sep 11 2017

%Y Cf. A035263, A056832.

%K nonn,mult

%O 1,2

%A _Benoit Cloitre_, Dec 30 2003

%E Keyword:mult added by _Andrew Howroyd_, Aug 01 2018

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Last modified June 20 01:36 EDT 2019. Contains 324223 sequences. (Running on oeis4.)