0,4

Write the numbers 1 through n in a circle, start at 1 and cross off every other number until only one number is left.

A version of the children's game "One potato, two potato, ...".

a(n)/A062383(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

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

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

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 10.

C. Groer, The mathematics of survival ..., Amer. Math. Monthly, 110 (No. 9, 2003), 812-825.

T. D. Noe, Table of n, a(n) for n=0..1000

J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197, ex. 34.

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

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

R. Stephan, Table of generating functions

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

To get a(n), write n in binary, rotate left 1 place.

G.f.: 2/(1-x) * ((3x-1)/(2-2x) - sum_{k>=1} 2^(k-1)*x^2^k). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 18 2003

a(n) = number of positive integers k < n such that n XOR k < n. a(n) = n - A035327(n). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 21 2006

a(n)=n for n=2^k-1, Zak Seidov, Dec 14, 2006

a(n) = n - A035327(n) [From K Spage (kevspage2001(AT)yahoo.co.uk), Oct 22 2009]

Contribution from Omar E. Pol (info(AT)polprimos.com), Jun 09 2009: (Start)

We can write the initial term followed by a triangle:

0;

1;

1,3;

1,3,5,7;

1,3,5,7,9,11,13,15;

1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31;

1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,...

(End)

Table[ FromDigits[ RotateLeft[ IntegerDigits[n, 2]], 2], {n, 0, 80}] (from Robert G. Wilson v)

(PARI) a(n)=sum(k=1, n, if(bitxor(n, k)<n, 1, 0)) (Hanna)

a(n) = 2 * A053645(n) + 1 = 2(n-msb(n))+1. - Marc LeBrun (mlb(AT)well.com), Jul 11 2001. Here "msb" = "most significant bit", A053644.

Cf. A054995, A038572, A053644, A053645, A088147, A088442.

Second column of triangle A032434. Diagonal of triangle A032434.

Cf. A035327.

Cf. A000079. [From Omar E. Pol (info(AT)polprimos.com), Jun 09 2009]

Sequence in context: A082082 A016646 A160552 this_sequence A114144 A050820 A133179

Adjacent sequences: A006254 A006255 A006256 this_sequence A006258 A006259 A006260

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Robert G. Wilson v, Sep 21, 2003