1,3

3 does not divide binomial(2s,s) if and only if s is a member of this sequence, where binomial(2s,s)= A000984(s) are the central binomial coefficients.

This is the "earliest" sequence obtained among nonnegative numbers by forbidding arithmetic subsequences of length 3 - Robert Craigen (craigenr(AT)cc.umanitoba.ca), Jan 29 2001

Complement of A074940. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 23 2003

Sums of distinct powers of 3. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 27 2003

n such that central trinomial coefficient A002426(n) == 1 (mod 3). - Emeric Deutsch and Bruce Sagan, Dec 04 2003

A039966(a(n)+1) = 1; A104406(n) = number of terms <= n.

Subsequence of A125292; A125291(a(n)) = 1 for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 26 2006

Also final value of n-1 written in base 2 and then read in base 3 and with finally the result translated in base 10. - Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Jun 23 2007

A081603(a(n)) = 0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 02 2008

Subsequence of A154314. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 07 2009]

a(n) modulo 2 is the Thue-Morse sequence A010060. [From Dennis Tseng (Dtseng(AT)cinci.rr.com), Jul 16 2009]

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, Theoretical Computer Sci., 98 (1992), 163-197.

R. K. Guy, Unsolved Problems in Number Theory, E10.

T. D. Noe, Table of n, a(n) for n=1..1024

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

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

J. W. Layman, Some Properties of a Certain Nonaveraging Sequence, J. Integer Sequences, Vol. 2, 1999, #4.

A. M. Odlyzko and R. P. Stanley, Some curious sequences constructed with the greedy algorithm, 1978, remark 1 (PDF, PS, TeX).

P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 228.

R. Stephan, Divide-and-conquer generating functions. I. Elementary sequences

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

R. Stephan, Table of generating functions

Z. Sunic, Tree morphisms, transducers and integer sequences

B. Vasic, K. Pedagani and M. Ivkovic, High-rate girth-eight low-density parity-check codes on rectangular integer lattices, IEEE Transactions on Communications, Vol. 52, Issue 8 (2004), 1248-1252.

Eric Weisstein's World of Mathematics, Central Binomial Coefficient

a(n+1) = sum( b(k)* 3^k ) for k=0..m and n = sum( b(k)* 2^k )

a(2n+1)=3a(n+1), a(2n+2)=a(2n+1)+1, a(0)=0.

a(n+1)=3*a(floor(n/2))+n-2*floor(n/2) - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 27 2003

G.f. x/(1-x) * Sum(k>=0, 3^k*x^2^k/(1+x^2^k)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 27 2003

n such that the coefficient of x^n is > 0 in prod (k>=0, 1+x^(3^k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 29 2003

a(n) = Sum_{k = 1..n-1} (1 + 3^A007814(k)) / 2 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 09 2005

If the offset were changed to zero, then: a(0)=0, a(n+1)=f(a(n)+1,f(a(n)+1) where f(x,y) = if x<3 and x<>2 then y else if x mod 3 = 2 then f(y+1, y+1) else f(floor(x/3),y). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 02 2008

a(6) = 12 because 6 = 0*2^0 +1*2^1 +1*2^2 = 2+4 and 12 = 0*3^0 +1*3^1 +1*3^2 = 3+9.

Table[FromDigits[IntegerDigits[k, 2], 3], {k, 60}]

(PARI) a(n)=n--; if(n<1, 0, if(n%2, a(n-1)+1, 3*a(n/2)))

(PARI) a(n)=n--; if(n<1, 0, 3*a(floor(n/2))+n-2*floor(n/2))

For generating functions Prod_{k>=0} (1+a*x^(b^k)) for the following values of (a,b) see: (1,2) A000012 and A000027, (1,3) A039966 and A005836, (1,4) A151666 and A000695, (1,5) A151667 and A033042, (2,2) A001316, (2,3) A151668, (2,4) A151669, (2,5) A151670, (3,2) A048883, (3,3) A117940, (3,4) A151665, (3,5) A151671, (4,2) A102376, (4,3) A151672, (4,4) A151673, (4,5) A151674.

a(n) = A005823(n)/2; a(n) = A003278(n)-1 = A033159(n)-2 = A033162(n)-3.

Cf. A005823, A032924, A054591, A007089, A081603, A081611, A000695, A007088, A033042-A033052, A074940, A083096. A002426.

Cf. A003278, A004793, A055246, A062548, A081601, A089118.

Row 3 of array A104257.

Sequence in context: A010388 A010400 A010439 this_sequence A054591 A121153 A059985

Adjacent sequences: A005833 A005834 A005835 this_sequence A005837 A005838 A005839

nonn,nice,easy

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

More terms from Emeric Deutsch and Bruce Sagan, Dec 04 2003

Offset corrected by N. J. A. Sloane (njas(AT)research.att.com), Mar 02 2008.

Edited by the Associate Editors of the OEIS, Apr 07 2009