A130253 - OEIS

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A130253

Number of Jacobsthal numbers (A001045) <=n.

1, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 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, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,2`
	COMMENTS	`Partial sums of the Jacobsthal indicator sequence (A105348). For n<>1, we have a(A001045(n))=n+1.`
	FORMULA	`a(n)=1+floor(log_2(3n+1))=ceiling(log_2(3n+2))=. Also true: a(n)=A130249(n)+1=A130250(n+1). G.f.: g(x)=1/(1-x)*sum{k>=0, x^A001045(k)}.`
	EXAMPLE	`a(9)=5 because there are 5 Jacobsthal numbers <=9 (0,1,1,3 and 5).`
	CROSSREFS	`For partial sums see A130254. Other related sequences A001045, A130249, A130250, A130253, A105348. Also A130233, A130235, A130241, A108852, A130245.` `Sequence in context: A058729 A021303 A130250 * A145288 A075324 A134993` `Adjacent sequences: A130250 A130251 A130252 * A130254 A130255 A130256`
	KEYWORD	`nonn`
	AUTHOR	`Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 20 2007`

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Last modified February 15 21:56 EST 2012. Contains 205860 sequences.