0,2

a(n) is the denominator of the form 2^k needed to make the ratio (2n-1)/2^k lie in the interval [1-2], i.e. such ratios are 1/1, 3/2, 5/4, 7/4, 9/8, 11/8, 13/8, 15/8, 17/16, 19/16, 21/16, ... where the numerators are A005408 (The odd numbers).

Let A_n be the upper triangular matrix in the group GL(n,2) that has zero entries below the diagonal and 1 elsewhere. For example for n=4 the matrix is / 1,1,1,1 / 0,1,1,1 / 0,0,1,1 / 0,0,0,1 /. The order of this matrix as an element of GL(n,2) is a(n-1). - Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 14 2001

A006257(n)/a(n) = (0, 0.1, 0.01, 0.11, 0.001, ...) enumerates all binary fractions in the unit interval [0, 1) - Fredrik Johansson, Aug 14 2006

a(n) = A142151(2*n)/2 + 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 15 2008

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009: (Start)

log(a(n))/log(2) = A029837(n+1)

(End)

a(n+1) = a(n) + A099894(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 06 2009]

Harry J. Smith, Table of n, a(n) for n=0,...,1000

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

a(1)=1 and a(n+1)=a(n)*ceil(n/a(n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 17 2002

G.f.: 1/(1-x) * (1 + sum_{k>=0} 2^k*x^2^k). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 18 2003

[seq(2^(floor_log_2(j)+1), j=0..127)]; or [seq(coerce1st_octave((2*j)+1), j=0..127)]; or [seq(a(j), j=0..127)];

coerce1st_octave := proc(r) option remember; if(r < 1) then coerce1st_octave(2*r); else if(r >= 2) then coerce1st_octave(r/2); else (r); fi; fi; end;

a := proc(n) option remember; if(0 = n) then RETURN(1); else RETURN(2*a(floor(n/2))); fi; end;

(PARI) { a=1; for (n=0, 1000, write("b062383.txt", n, " ", a*=ceil((n + 1)/a)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 06 2009]

Apart from the initial term, A062383[n] = 2* A053644[n]. MASKTRANSi(A062383) seems to give a signed form of A038712. (See identities at A053644). floor_log_2 given in A054429.

Equals A003817(n)+1. Cf. A002884.

Bisection of A065285. Cf. A076877.

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)

Equals for n>=1 the r(n) sequence of A160464.

(End)

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009: (Start)

Equals the r(n) sequence of A162440 for n>=1.

(End)

Sequence in context: A093820 A095400 A098820 this_sequence A034583 A076347 A140513

Adjacent sequences: A062380 A062381 A062382 this_sequence A062384 A062385 A062386

nonn,frac

Antti Karttunen Jun 19 2001