A130250 Minimal index k of a Jacobsthal number such that A001045(k) >= n (the 'upper' Jacobsthal inverse).

0, 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

Offset

0,3

Comments

Inverse of the Jacobsthal sequence (A001045), nearly, since a(A001045(n))=n except for n=2 (see A130249 for another version). a(n+1) is equal to the partial sum of the Jacobsthal indicator sequence (see A105348).

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Formula

a(n) = ceiling(log_2(3n-1)) = 1 + floor(log_2(3n-2)) for n >= 1.

a(n) = A130249(n-1) + 1 = A130253(n-1) for n >= 1.

G.f.: (x/(1-x))*Sum_{k>=0} x^A001045(k).

Example

a(10)=5 because A001045(5) = 11 >= 10, but A001045(4) = 5 < 10.

Mathematica

Table[If[n==0, 0, Ceiling[Log[2, 3*n-1]]], {n, 0, 120}] (* G. C. Greubel, Mar 18 2023 *)

Prog

(Magma) [0] cat [Ceiling(Log(2, 3*n-1)): n in [1..120]]; // G. C. Greubel, Mar 18 2023
(SageMath)
def A130250(n): return 0 if (n==0) else ceil(log(3*n-1, 2))
[A130250(n) for n in range(121)] # G. C. Greubel, Mar 18 2023

Crossrefs

For partial sums see A130252.

Cf. A001045, A105348, A130234, A130242, A130249, A130253.

Sequence in context: A303821 A240622 A364883 * A130253 A145288 A075324

Adjacent sequences: A130247 A130248 A130249 * A130251 A130252 A130253

Keyword

nonn

Author

Hieronymus Fischer, May 20 2007

Status

approved