A070885 a(n) = (3/2)*a(n-1) if a(n-1) is even; (3/2)*(a(n-1)+1) if a(n-1) is odd.

1, 3, 6, 9, 15, 24, 36, 54, 81, 123, 186, 279, 420, 630, 945, 1419, 2130, 3195, 4794, 7191, 10788, 16182, 24273, 36411, 54618, 81927, 122892, 184338, 276507, 414762, 622143, 933216, 1399824, 2099736, 3149604, 4724406, 7086609, 10629915

Offset: 1

Author

Eric W. Weisstein, May 14 2002

Keywords

• nonn

Comments

The smallest positive number such that A024629(a(n)) has n digits, per page 9 of the Tanton reference in Links. - Glen Whitney, Sep 17 2017

References

• Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, 2002, p. 123.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• B. Chen, R. Chen, J. Guo, S. Lee et al., On Base 3/2 and its Sequences, arXiv:1808.04304 [math.NT], 2018.
• James Tanton, Exploding Dots, Chapter 9
• Eric Weisstein's World of Mathematics, Wolfram Sequences

Crossrefs

The constant K is 2/3*K(3) (see A083286). - Ralf Stephan, May 29 2003

Cf. A003312.

Cf. A081848.

Cf. A205083 (parity of terms).

Programs

Haskell

a070885 n = a070885_list !! (n-1)
a070885_list = 1 : map (flip (*) 3 . flip div 2 . (+ 1)) a070885_list
-- Reinhard Zumkeller, Sep 05 2014

Maple

A070885 := proc(n)
    option remember;
    if n = 1 then
        return 1;
    elif type(procname(n-1),'even') then
        procname(n-1) ;
    else
        procname(n-1)+1 ;
    end if;
    %*3/2 ;
end proc:
seq(A070885(n),n=1..80) ; # R. J. Mathar, Jun 18 2018

Mathematica

NestList[If[EvenQ[#],3/2 #,3/2 (#+1)]&,1,40] (* Harvey P. Dale, May 18 2018 *)

Python

from itertools import islice
def A070885_gen(): # generator of terms
    a = 1
    while True:
        yield a
        a += (a+1>>1)+(a&1)
A070885_list = list(islice(A070885_gen(),70)) # Chai Wah Wu, Sep 20 2022

Formula

For n > 1, a(n) = 3*A061419(n) = 3*floor(K*(3/2)^n) where K=1.08151366859... - Benoit Cloitre, Aug 18 2002

a(n) = 3*ceiling(a(n-1)/2). - Benoit Cloitre, Apr 25 2003

a(n+1) = a(n) + A081848(n), for n > 1. - Reinhard Zumkeller, Sep 05 2014