

A054414


a(n) = 1 + floor(n/(1log(2)/log(3))).


8



1, 3, 6, 9, 11, 14, 17, 19, 22, 25, 28, 30, 33, 36, 38, 41, 44, 47, 49, 52, 55, 57, 60, 63, 66, 68, 71, 74, 76, 79, 82, 84, 87, 90, 93, 95, 98, 101, 103, 106, 109, 112, 114, 117, 120, 122, 125, 128, 131, 133, 136, 139, 141, 144, 147, 150, 152, 155, 158, 160, 163
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OFFSET

0,2


COMMENTS

These numbers appear in connection with the 3x+1 problem.
Also, numbers n such that the first digit in ternary expansion on 2^n is 2. N. J. A. Sloane conjectured that, for any integer n >=15, 2^n always has a 0 in its ternary expansion.  Mohammed Bouayoun (Mohammed.bouayoun(AT)sanef.com), Apr 24 2006
Except for 1, this is the complement of A020914 and therefore these two form a pair of Beatty sequences.  Robert G. Wilson v, May 25 2014


LINKS



EXAMPLE

a(5) = 1 + floor(5/(1log(2)/log(3)))= 1 + floor(5/0.3690702464...)= 1 + floor(13.54...) = 14.


MAPLE

Digits := 500: it := evalf(ln(2)/ln(3)): for n from 0 to 200 do printf(`%d, `, 1+floor(n/(1it))) od:


MATHEMATICA

Do[If[First[IntegerDigits[2^n, 3]] == 2, Print[n]], {n, 1, 200}] (* Mohammed Bouayoun (Mohammed.bouayoun(AT)sanef.com), Apr 24 2006 *)
f[n_]:=Floor[1+n/(1(Log[2]/Log[3]))]; Array[f, 105] (* Robert G. Wilson v, May 25 2014 *)


PROG

(PARI) alist(N) = my(a=1/2, b=1, r=1); vector(N, i, a*=4; b*=3; r+=2; if(a>b, a*=2; b*=3; r++); r); \\ Ruud H.G. van Tol, Jan 21 2024 (with help from the pariusers mailing list)


CROSSREFS



KEYWORD

easy,nonn


AUTHOR

B. Schaaf (m.m.schaafvisch(AT)wxs.nl), May 20 2000


EXTENSIONS

Erroneous formula a(n) =? A083088(n) + n  1 deleted Jan 30 2008


STATUS

approved



