login
Number of numbers whose base-3/2 expansion (see A024629) has n digits.
35

%I #48 Sep 21 2022 01:42:21

%S 3,3,3,6,9,12,18,27,42,63,93,141,210,315,474,711,1065,1599,2397,3597,

%T 5394,8091,12138,18207,27309,40965,61446,92169,138255,207381,311073,

%U 466608,699912,1049868,1574802,2362203,3543306,5314959,7972437,11958657

%N Number of numbers whose base-3/2 expansion (see A024629) has n digits.

%C Run lengths in A246435. - _Reinhard Zumkeller_, Sep 05 2014

%H Reinhard Zumkeller, <a href="/A081848/b081848.txt">Table of n, a(n) for n = 1..1000</a>

%H B. Chen, R. Chen, J. Guo, S. Lee et al., <a href="http://arxiv.org/abs/1808.04304">On Base 3/2 and its sequences</a>, arXiv:1808.04304 [math.NT], 2018.

%H J. S. Tanton, <a href="https://web.archive.org/web/20110108124656/http://www.themathcircle.org/researchproblems.php">A collection of research problems</a>.

%F For n > 1, a(n) = A070885(n+1) - A070885(n). - _Tom Edgar_, Jun 25 2014

%F a(n) = 3*A073941(n). - _Tom Edgar_, Jul 21 2014

%e a(1) = 3 because 0, 1 and 2 each have 1 digit.

%o (Haskell)

%o a081848 n = a081848_list !! (n-1)

%o a081848_list = 3 : tail (zipWith (-) (tail a070885_list) a070885_list)

%o -- _Reinhard Zumkeller_, Sep 05 2014

%o (Python)

%o from itertools import islice

%o def A081848_gen(): # generator of terms

%o yield (a:=3)

%o while True:

%o yield (b:=(a+1>>1)+(a&1))

%o a += b

%o A081848_list = list(islice(A081848_gen(),70)) # _Chai Wah Wu_, Sep 20 2022

%Y Cf. A024629, A070885, A073941, A246435.

%K easy,nonn,base

%O 1,1

%A _N. J. A. Sloane_, Apr 13 2003

%E More terms from _David Wasserman_, Jun 28 2004

%E Edited by _Charles R Greathouse IV_, Aug 02 2010