0,3

Starting with a(1)=0 mirror all initial 2^k segments and increase by one.

a(n) gives the net rotation (measured in right angles) after taking n steps along a dragon curve. - Christopher Hendrie (hendrie(AT)acm.org), Sep 11 2002

This sequence generates A082410: (0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1...) and A014577; identical to the latter except starting 1, 1, 0...; by writing a "1" if a(n+1) > a(n); if not, write "0". E.g. A014577(2) = 0, since a(3) < a(2), or 1 < 2. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 20 2003

Starting with "1" = partial sums of A034947: (1, 1, -1, 1, 1, -1, -1, 1, 1, 1,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 23 2008

The composer Per Norgard's name is also written in the OEIS as Per Noergaard.

J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.

Flajolet and Ramshaw, A note on Gray code..., SIAM J. Comput. 9 (1980), 142-158.

Jeffrey Shallit, The mathematics of Per Noergaard's rhythmic infinity system, Fib. Q., 43 (2005), 262-268.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..10000

Joerg Arndt, Fxtbook

J.-P. Allouche, J. Shallit, The Ring of k-regular Sequences, II

P. Flajolet et al., Mellin Transforms And Asymptotics: Digital Sums, Theoret. Computer Sci. 23 (1994), 291-314.

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

R. Stephan, Table of generating functions

Index entries for "core" sequences

a(2^k + i) = a(2^k - i + 1) + 1 for k >= 0 and 0 < i <= 2^k. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 14 2001

a(2n+1) = 2a(n)-a(2n)+1, a(4n) = a(2n), a(4n+2) = 1+a(2n+1).

a(j+1) = a(j) + (-1)^A014707[j] - Christopher Hendrie (hendrie(AT)acm.org), Sep 11 2002

G.f.: 1/(1-x) * sum(k>=0, x^2^k/(1+x^2^(k+1))). - Ralf Stephan, May 2 2003

Delete the 0, make subsets of 2^n terms; and reverse the terms in each subset to generate A088696. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 19 2003

a(0)=0, a(2n) = a(n) + [n odd], a(2n+1) = a(n) + [n even]. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 20 2003

a(n) = sum(k=1, n, (-1)^((k/2^A007814(k)-1)/2)) = sum(k=1, n, (-1)^A025480(k-1)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 29 2003

A005811 := proc(n) local i, b, ans; ans := 1; b := convert(n, base, 2); for i from 2 to nops(b) do if b[ i-1 ]<>b[ i ] then ans := ans+1 fi od; RETURN(ans); end; [ seq(A005811(i), i=1..50) ];

Table[ Length[ Length/@Split[ IntegerDigits[ n, 2 ] ] ], {n, 1, 255} ]

(PARI) a(n)=sum(k=1, n, (-1)^((k/2^valuation(k, 2)-1)/2))

Cf. A056539, A014707, A014577, A082410.

A000975 gives records. - Oliver Kosut (vern(AT)mit.edu), May 06 2002

a(n) = A037834(n)+1.

a(n) = A069010(n) + A033264(n) (from Ralf Stephan)

Cf. A034947.

Sequence in context: A088696 A004738 A043554 this_sequence A008342 A002850 A111944

Adjacent sequences: A005808 A005809 A005810 this_sequence A005812 A005813 A005814

easy,nonn,core,nice

N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit, Simon Plouffe

Additional description from Wouter Meeussen (wouter.meeussen(AT)pandora.be)