A130249 - OEIS

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A130249

Maximal index k of a Jacobsthal number such that A001045(k)<=n (the 'lower' Jacobsthal inverse).

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: A238701 A238134 A143489 * A061071 A122258 A068509` `Adjacent sequences: A130246 A130247 A130248 * A130250 A130251 A130252`
	KEYWORD	`nonn`
	AUTHOR	`Hieronymus Fischer, May 20 2007`
	STATUS	`approved`

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Last modified March 7 03:27 EST 2014. Contains 238504 sequences.