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A130249
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Maximal index k of a Jacobsthal number such that A001045(k)<=n (the 'lower' Jacobsthal inverse).
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13
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0, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 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, 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
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OFFSET
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0,2
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COMMENTS
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Inverse of the Jacobsthal sequence (A001045), nearly, since a(A001045(n))=n except for n=1 (see A130250 for another version). a(n)+1 is equal to the partial sum of the Jacobsthal indicator sequence (see A105348).
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..10000
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FORMULA
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a(n) = floor(log_2(3n+1)).
a(n) = A130250(n+1) - 1 = A130253(n) - 1.
G.f.: 1/(1-x)*(Sum_{k>=1} x^A001045(k)).
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EXAMPLE
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a(12)=5, since A001045(5)=11<=12, but A001045(6)=21>12.
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MATHEMATICA
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Table[Floor[Log[2, 3*n + 1]], {n, 0, 50}] (* G. C. Greubel, Jan 08 2018 *)
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PROG
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(PARI) for(n=0, 30, print1(floor(log(3*n+1)/log(2)), ", ")) \\ G. C. Greubel, Jan 08 2018
(MAGMA) [Floor(Log(3*n+1)/Log(2)): n in [0..30]]; // G. C. Greubel, Jan 08 2018
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CROSSREFS
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For partial sums see A130251. Other related sequences A130250, A130253, A105348. A001045, A130233, A130241.
Sequence in context: A143489 A274102 A261100 * A286105 A061071 A122258
Adjacent sequences: A130246 A130247 A130248 * A130250 A130251 A130252
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KEYWORD
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nonn
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AUTHOR
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Hieronymus Fischer, May 20 2007
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STATUS
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approved
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