

A130253


Number of Jacobsthal numbers (A001045) <=n.


12



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
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OFFSET

0,2


COMMENTS

Partial sums of the Jacobsthal indicator sequence (A105348).
For n<>1, we have a(A001045(n))=n+1.


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000


FORMULA

a(n) = floor(log_2(3n+1)) + 1 = ceiling(log_2(3n+2)).
a(n) = A130249(n) + 1 = A130250(n+1).
G.f.: 1/(1x)*(Sum_{k>=0} x^A001045(k)).


EXAMPLE

a(9)=5 because there are 5 Jacobsthal numbers <=9 (0,1,1,3 and 5).


MATHEMATICA

Table[1+Floor[Log[2, 3n+1]], {n, 0, 100}] (* Harvey P. Dale, Jul 03 2013 *)


PROG

(PARI) a(n)=logint(3*n+1, 2)+1 \\ Charles R Greathouse IV, Oct 03 2016
(MAGMA) [Ceiling(Log(3*n+2)/Log(2)): n in [0..30]]; // G. C. Greubel, Jan 08 2018


CROSSREFS

For partial sums see A130252. Other related sequences A001045, A130249, A130250, A130253, A105348. Also A130233, A130235, A130241, A108852, A130245.
Sequence in context: A303821 A240622 A130250 * A145288 A075324 A134993
Adjacent sequences: A130250 A130251 A130252 * A130254 A130255 A130256


KEYWORD

nonn,easy


AUTHOR

Hieronymus Fischer, May 20 2007


STATUS

approved



