1,2

Minimal with respect to property that parity of number of 1's in binary expansion alternates.

Minimal with respect to property that sequence is double of its complement.

If n appears then 2n does not.

Increasing sequence of positive integers n such that A035263(n)=1 (from paper by Allouche et al.). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 15 2003

a(n) is an odious number (see A000069) for n odd; a(n) is an evil number (see A001969) for n even. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 16 2004

Indices of odd numbers in A007913, in A001511. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 27 2004

Partial sums of A026465. - Paul Barry (pbarry(AT)wit.ie), Dec 09 2004

A121701(2*a(n)) = A121701(a(n)); A096268(a(n)-1) = 0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 16 2006

A different permutation of the same terms may be found in A141290 and the accompanying array. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 14 2008

a(n) = n-th clockwise Tower of Hanoi move; counterclockwise if not in the sequence. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 14 2008

Indices of terms of Thue-Morse sequence A010060 which are different from the previous term. [From Tanya Khovanova (tanyakh(AT)yahoo.com), Jan 06 2009]

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

L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Representations for a special sequence, Fib. Quart., 10 (1972), 499-518, 550.

Michael Domaratzki, Trajectory-based codes, Acta Informatica, Volume 40, Numbers 6-7 / May, 2004. [From N. J. A. Sloane, Jul 10 2009]

Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.

Problem E2850, Amer. Math. Monthly, 87 (1980), 671.

T. D. Noe, Table of n, a(n) for n=1..1000

J.-P. Allouche, Andre Arnold, Jean Berstel, Srecko Brlek, William Jockusch, Simon Plouffe and Bruce E. Sagan, A sequence related to that of Thue-Morse, Discrete Math., 139 (1995), 455-461.

J.-P. Allouche and J. O. Shallit, The Ubiquitous Prouhet-Thue-Morse Sequence, in C. Ding. T. Helleseth and H. Niederreiter, eds., Sequences and Their Applications: Proceedings of SETA '98, Springer-Verlag, 1999, pp. 1-16.

J.-P. Allouche, J. Shallit and G. Skordev, Self-generating sets, integers with missing blocks and substitutions, Discrete Math. 292 (2005) 1-15.

E. Deutsch and B. E. Sagan, Congruences for Catalan and Motzkin numbers and related sequences, J. Num. Theory 117 (2006), 191-215.

A. S. Fraenkel, New games related to old and new sequences, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004.

A. S. Fraenkel, Home Page

Index entries for sequences related to binary expansion of n

a(0)=1; for n>=0, a(n+1) = a(n)+1 if (a(n)+1)/2 is not already in the sequence, = a(n)+2 otherwise.

Lim n ->infinity a(n)/n = 3/2 - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 13 2002

a(n)=sum(k=1, n, A026465(k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 31 2003

a(n+1) = (if a(n) mod 4 = 3 then A007814(a(n) + 1) mod 2 else a(n) mod 2) + a(n) + 1; a(1) = 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 03 2003

a(A003157(n)) is even. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 22 2004

Sequence consists of numbers of the form 4^i*(2j+1), i>=0, j>=0. - Jon Perry (perry(AT)globalnet.co.uk), Jun 06 2004

G.f.: (1/(1-x))Product{k>=1, 1+x^A001045(k)}. - Paul Barry (pbarry(AT)wit.ie), Dec 09 2004

1=1 (odd), 3=11 (even), 4=100 (odd), 5=101 (even), 7=111 (odd), ...

f[n_Integer] := Block[{k = n, c = 0}, While[ EvenQ[k], c++; k /= 2]; c]; Select[ Range[105], EvenQ[ f[ # ]] & ]

(PARI) a(n)=if(n<2, n>0, n=a(n-1); until(valuation(n, 2)%2==0, n++); n)

Indices of even numbers in A007814. Complement of A036554, also one-half of A036554. Cf. A001285, A010060.

Equals A056196(n)/8.

Sequence in context: A156246 A136014 A112930 this_sequence A141259 A047501 A035242

Adjacent sequences: A003156 A003157 A003158 this_sequence A003160 A003161 A003162

nonn,nice,easy,eigen

N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

Additional comments from Michael Somos.