

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
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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(n1), 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



