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

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A087808 a(0) = 0; a(2n) = 2a(n), a(2n+1) = a(n) + 1. 13
0, 1, 2, 2, 4, 3, 4, 3, 8, 5, 6, 4, 8, 5, 6, 4, 16, 9, 10, 6, 12, 7, 8, 5, 16, 9, 10, 6, 12, 7, 8, 5, 32, 17, 18, 10, 20, 11, 12, 7, 24, 13, 14, 8, 16, 9, 10, 6, 32, 17, 18, 10, 20, 11, 12, 7, 24, 13, 14, 8, 16, 9, 10, 6, 64, 33, 34, 18, 36, 19, 20, 11, 40, 21, 22, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.

FORMULA

a(n) = A135533(n)+1-2^(A000523(n)+1-A000120(n)). - Don Knuth, Mar 01 2008

From Antti Karttunen, Oct 07 2016: (Start)

a(n) = A048675(A005940(n+1)).

For all n >= 0, a(A003714(n)) = A048679(n).

For all n >= 0, a(A277020(n)) = n.

(End)

MAPLE

S := 2; f := proc(n) global S; option remember; if n=0 then RETURN(0); fi; if n mod 2 = 0 then RETURN(S*f(n/2)); else f((n-1)/2)+1; fi; end;

MATHEMATICA

a[0]=0; a[n_] := a[n] = If[EvenQ[n], 2*a[n/2], a[(n-1)/2]+1]; Array[a, 76, 0] (* Jean-François Alcover, Aug 12 2017 *)

PROG

(PARI) a(n)=if(n<1, 0, if(n%2==0, 2*a(n/2), a((n-1)/2)+1))

(Haskell)

import Data.List (transpose)

a087808 n = a087808_list !! n

a087808_list = 0 : concat

   (transpose [map (+ 1) a087808_list, map (* 2) $ tail a087808_list])

-- Reinhard Zumkeller, Mar 18 2015

(Scheme) (define (A087808 n) (cond ((zero? n) n) ((even? n) (* 2 (A087808 (/ n 2)))) (else (+ 1 (A087808 (/ (- n 1) 2)))))) ;; Antti Karttunen, Oct 07 2016

CROSSREFS

This is Guy Steele's sequence GS(5, 4) (see A135416).

A048678(k) is where k appears first in the sequence.

Cf. A000120, A003714, A004718, A005940, A048675, A048679, A080100, A090639.

A left inverse of A277020.

Cf. also A277006.

Sequence in context: A083742 A107331 A283187 * A217754 A094950 A087874

Adjacent sequences:  A087805 A087806 A087807 * A087809 A087810 A087811

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Oct 14 2003

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 19 01:27 EST 2017. Contains 294912 sequences.