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A130249 Maximal index k of a Jacobsthal number such that A001045(k)<=n (the 'lower' Jacobsthal inverse). 13
0, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Inverse of the Jacobsthal sequence (A001045), nearly, since a(A001045(n))=n except for n=1 (see A130250 for another version). a(n)+1 is equal to the partial sum of the Jacobsthal indicator sequence (see A105348).

LINKS

Table of n, a(n) for n=0..100.

FORMULA

a(n)=floor(log_2(3n+1)). Also true: a(n)=A130250(n+1)-1=A130253(n)-1. G.f.: g(x)=1/(1-x)*sum{k>=1, x^A001045(k)}.

EXAMPLE

a(12)=5, since A001045(5)=11<=12, but A001045(6)=21>12.

CROSSREFS

For partial sums see A130251. Other related sequences A130250, A130253, A105348. A001045, A130233, A130241.

Sequence in context: A143489 A274102 A261100 * A061071 A122258 A263089

Adjacent sequences:  A130246 A130247 A130248 * A130250 A130251 A130252

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, May 20 2007

STATUS

approved

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Last modified December 11 05:09 EST 2016. Contains 279034 sequences.