

A130253


Number of Jacobsthal numbers (A001045) <=n.


14



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
Dorin Andrica, Ovidiu Bagdasar, and George Cătălin Tųrcąs, On some new results for the generalised Lucas sequences, An. Şt. Univ. Ovidius Constanţa (Romania, 2021) Vol. 29, No. 1, 1736.


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



