login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A073941 a(n) = ceiling((Sum_{k=1..n-1} a(k)) / 2); a(1)=1. 98
1, 1, 1, 2, 3, 4, 6, 9, 14, 21, 31, 47, 70, 105, 158, 237, 355, 533, 799, 1199, 1798, 2697, 4046, 6069, 9103, 13655, 20482, 30723, 46085, 69127, 103691, 155536, 233304, 349956, 524934, 787401, 1181102, 1771653, 2657479, 3986219, 5979328, 8968992 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) is the number of even integers that have n-1 digits when written in base 3/2. For example, there are 2 even integers that use three digits in base 3/2: 6 and 8: they are written as 210 and 212, respectively. - Tanya Khovanova and PRIMES STEP Senior group, Jun 03 2018

LINKS

T. D. Noe, Table of n, a(n) for n = 1..500

B. Chen, R. Chen, J. Guo, S. Lee et al, On Base 3/2 and its sequences, arXiv:1808.04304 [math.NT], 2018.

Tom Edgar, Hailey Olafson, James Van Alstine, Approximating the Fibonacci Sequence, Integers 16 (2016), #A63.

FORMULA

a(n) = ceiling(c*(3/2)^n-1/2) where c = 0.3605045561966149591015446628665... - Benoit Cloitre, Nov 22 2002

If 2^m divides a(i) then 2^(m-1)*3^1 divides a(i+1) and so on... until finally, 3^m divides a(i+m). - Ralf Stephan, Apr 20 2003

a(n) = A081848(n)/3. - Tom Edgar, Jul 21 2014

a(n) = A005428(n-2). - Tanya Khovanova and PRIMES STEP Senior group, Jun 03 2018

MATHEMATICA

f[s_] := Append[s, Ceiling[Plus @@ s/2]]; Nest[f, {1}, 41] (* Robert G. Wilson v, Jul 07 2006 *)

PROG

(PARI) v=vector(100); s=v[1]=1; for(i=2, #v, s+=(v[i]=(s+1)\2)); v \\ Charles R Greathouse IV, Feb 11 2011

(Haskell)

a073941 n = a073941_list !! (n-1)

a073941_list = 1 : f [1] where

   f xs = x' : f (x':xs) where x' = (1 + sum xs) `div` 2

-- Reinhard Zumkeller, Oct 26 2011

CROSSREFS

Same as log_2(A082125(n)), for n > 2. - Ralf Stephan, Apr 16 2002

Apart from initial term, same as A005428, which has further information.

a(n+4) = A079719(n)+2. Cf. A082416.

Partial sums for various start indices are in A006999, A061419, A061418. - Ralf Stephan, Apr 17 2003

Is this the same as A081848/3?

The constant c is (2/9)*K(3) (see A083286). - Ralf Stephan, May 29 2003

Sequence in context: A212464 A302016 A078620 * A005428 A143951 A292800

Adjacent sequences:  A073938 A073939 A073940 * A073942 A073943 A073944

KEYWORD

nonn,nice

AUTHOR

Reinhard Zumkeller, Nov 20 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 20 19:51 EDT 2019. Contains 326155 sequences. (Running on oeis4.)