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

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, 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, 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

Offset

1,2

Comments

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).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65536

Index entries for sequences related to binary expansion of n.

Index entries for sequences that are fixed points of mappings.

Formula

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

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 7/3. - Amiram Eldar, Nov 28 2022

From Amiram Eldar, Jan 04 2023: (Start)

Multiplicative with a(2^e) = 5 if e is odd, and 1 if e is even, a(p^e) = 1 for p >= 3.

Dirichlet g.f.: zeta(s)*(2^s+5)/(2^s+1). (End)

Mathematica

a[n_] := Mod[IntegerExponent[n, 2], 2] * 4 + 1; Array[a, 100] (* Amiram Eldar, Nov 28 2022 *)

Prog

(PARI) a(n)=numerator(2/n*(4^n-1)*bernfrac(2*n))%6
(PARI) a(n)=valuation(n, 2)%2 * 4 + 1; \\ Andrew Howroyd, Aug 01 2018
(Scheme)
(define (A035263 n) (let loop ((n n) (i 1)) (cond ((odd? n) (modulo i 2)) (else (loop (/ n 2) (+ 1 i))))))
(define (A089608 n) (- 5 (* 4 (A035263 n))))
;; Antti Karttunen, Sep 11 2017

Crossrefs

Cf. A002425, A035263, A056832.

Sequence in context: A323921 A293235 A066803 * A250131 A100615 A293897

Adjacent sequences: A089605 A089606 A089607 * A089609 A089610 A089611

Keyword

nonn,mult

Author

Benoit Cloitre, Dec 30 2003

Extensions

Keyword:mult added by Andrew Howroyd, Aug 01 2018

Status

approved