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 A087808 a(0) = 0; a(2n) = 2a(n), a(2n+1) = a(n) + 1. 26
 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 (Python) from functools import lru_cache @lru_cache(maxsize=None) def A087808(n): return 0 if n == 0 else A087808(n//2) + (1 if n % 2 else A087808(n//2)) # Chai Wah Wu, Mar 08 2022 CROSSREFS This is Guy Steele's sequence GS(5, 4) (see A135416); compare GS(4, 5): A135529. 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: A283187 A324391 A357978 * A217754 A319397 A094950 Adjacent sequences: A087805 A087806 A087807 * A087809 A087810 A087811 KEYWORD nonn,easy AUTHOR Ralf Stephan, Oct 14 2003 STATUS approved

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Last modified December 5 15:27 EST 2022. Contains 358588 sequences. (Running on oeis4.)