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A022921 Number of 2^m between 3^n and 3^(n+1). 8
1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Represents increments between successive terms of allowable dropping times in the Collatz (3x+1) problem. That is, a(n) = A020914(n+1) - A020914(n). - K. Spage, Oct 23 2009

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

Mike Winkler, The algorithmic structure of the finite stopping time behavior of the 3x+ 1 function, arXiv:1709.03385 [math.GM], 2017.

FORMULA

a(n) = floor((n+1)*log_2(3)) - floor(n*log_2(3)).

a(n) = A122437(n+2) - A122437(n+1) - 1. - K. Spage, Oct 23 2009

First differences of A020914. - Robert G. Wilson v, May 25 2014

First differences of A056576. - L. Edson Jeffery, Dec 12 2014

MAPLE

Digits := 100: c1 := log(3.)/log(2.): A022921 := n->floor((n+1)*c1)-floor(n*c1);

seq(ilog2(3^(n+1)) - ilog2(3^n), n=0 .. 1000); # Robert Israel, Dec 11 2014

MATHEMATICA

i2 = 1; Table[p = i2; While[i2++; 2^i2 < 3^(n + 1)]; i2 - p, {n, 0, 98}] (* T. D. Noe, Feb 28 2014 *)

f[n_] := Floor[ Log2[ 3^n] + 1]; Differences@ Array[f, 106, 0] (* Robert G. Wilson v, May 25 2014 *)

CROSSREFS

Cf. A020914, A056576, A076227, A100982, A122437.

See also A020857 (decimal expansion of log_2(3)).

Sequence in context: A306717 A195969 A023518 * A080763 A245920 A165413

Adjacent sequences:  A022918 A022919 A022920 * A022922 A022923 A022924

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified May 21 22:24 EDT 2019. Contains 323467 sequences. (Running on oeis4.)