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A130250
Minimal index k of a Jacobsthal number such that A001045(k) >= n (the 'upper' Jacobsthal inverse).
8
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
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.
Sequence in context: A303821 A240622 A364883 * A130253 A145288 A075324
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, May 20 2007
STATUS
approved