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A236313 Recurrence: a(2n) = 3a(n)-1, a(2n+1) = 1. 3
1, 2, 1, 5, 1, 2, 1, 14, 1, 2, 1, 5, 1, 2, 1, 41, 1, 2, 1, 5, 1, 2, 1, 14, 1, 2, 1, 5, 1, 2, 1, 122, 1, 2, 1, 5, 1, 2, 1, 14, 1, 2, 1, 5, 1, 2, 1, 41, 1, 2, 1, 5, 1, 2, 1, 14, 1, 2, 1, 5, 1, 2, 1, 365, 1, 2, 1, 5, 1, 2, 1, 14, 1, 2, 1, 5, 1, 2, 1, 41, 1, 2, 1, 5, 1, 2, 1, 14, 1, 2, 1, 5, 1, 2, 1, 122, 1, 2, 1, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First differences of Stanley sequence S(0,1) (A005836) and S(1,2) (A003278).

In the binary expansion of n, delete everything left of the rightmost 1 bit, then interpret as ternary, add one, and divide by 2.

A007051 is this sequence in strictly increasing order. - Max Barrentine, Sep 11 2015

Empirical: a(n) is the smallest natural number k such that no two adjacent subsequences t and u consisting of consecutive entries of (a(1), a(2), ..., a(n-1), k) are such that the sum of the entries of t is equal to the sum of the entries of u. For example, according to this definition, a(4) cannot be equal to 1, 2, 3, or 4. - John M. Campbell, Mar 20 2017

Multiplicative with a(2^e) = (1 + 3^e)/2, a(p^e) = 1 for odd prime p. - Andrew Howroyd, Jul 31 2018

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = (1/2)*(1 + 3^A007814(n)) = A007051(A007814(n)).

a(n) = (1/2)*A061393(n), for n>=1.

MATHEMATICA

t = {1}; Do[If[OddQ[n], AppendTo[t, 1], AppendTo[t, 3*t[[n/2]] - 1]], {n, 2, 100}]; t (* T. D. Noe, Apr 10 2014 *)

a[n_] := a[n] =If[OddQ@ n, 1, 3 a[n/2] - 1]; Array[a, 92] (* Robert G. Wilson v, Jul 31 2018 *)

PROG

(PARI) a(n)=(1+3^valuation(n, 2))/2

(MAGMA) [(1+3^Valuation(n, 2))/2: n in [1..100]]; // Bruno Berselli, Jan 22 2014

CROSSREFS

Cf. A003278, A005836, A006519, A007051, A007814, A061393, A093682.

Sequence in context: A246964 A157334 A320667 * A222481 A200778 A132601

Adjacent sequences:  A236310 A236311 A236312 * A236314 A236315 A236316

KEYWORD

nonn,mult

AUTHOR

Ralf Stephan, Jan 22 2014

STATUS

approved

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Last modified September 30 12:21 EDT 2020. Contains 337439 sequences. (Running on oeis4.)