0,2

Another definition: a(0) = 0, a(1) = 2; for n > 1, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) is a multiple of 3". - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 14 2003

Yet another definition: a(0) = 0, a(1)=2; for n > 1, a(n) is the smallest integer > a(n-1) satisfying "if n is in the sequence, a(n)==0 (mod 3)" ("only if" omitted).

This sequence is the case m = 2 of the following family: a(1, m) = m, a(n, m) is the smallest integer > a(n-1, m) satisfying "if n is in the sequence, a(n, m) == 0 (mod (2m-1))". The general formula is: for any k >= 0, for j = -m*(2m-1)^k, ..., -1, 0, 1, ..., m*(2m-1)^k, a((m-1)*(2*m-1)^k+j) = (2*m-1)^(k+1)+m*j+(m-1)*abs(j).

Numbers whose base 3 representation starts with 2 or ends with 0. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 17 2006

J.-P. Allouche, N. Rampersad and J. Shallit, On integer sequences whose first iterates are linear, Aequationes Math. 69 (2005), 114-127

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

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

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)

J. Shallit, Number theory and formal languages, in D. A. Hejhal, J. Friedman, M. C. Gutzwiller and A. M. Odlyzko, eds., Emerging Applications of Number Theory, IMA Volumes in Mathematics and Its Applications, V. 109, Springer-Verlag, 1999, pp. 547-570.

Index entries for sequences of the a(a(n)) = 2n family

For any k>=0, a(3^k - j) = 2*3^k - 3j, 0 <= j <= 3^(k-1); a(3^k + j) = 2*3^k + j, 0 <= j <= 3^k.

a(3n)=3a(n), a(3n+1)=2a(n)+a(n+1), a(3n+2)=a(n)+2a(n+1), n>0. Also a(n+1)-2*a(n)+a(n-1)= { 2 if n=3^k, -2 if n=2*3^k, otherwise 0}, n>1. - Michael Somos, May 03 2000.

a(n) = n + A006166(n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 01 2003

9 is in the sequence and the smallest multiple of 3 greater than a(9-1)=a(8)=15 is 18. Hence a(9)=18

(PARI) a(n)=if(n<3, n+(n>0), (3-(n%3))*a(n\3)+(n%3)*a(n\3+1))

Cf. A079000, A007378, A079351.

Sequence in context: A037460 A161824 A102806 this_sequence A132188 A060132 A059590

Adjacent sequences: A003602 A003603 A003604 this_sequence A003606 A003607 A003608

nonn

Jim Propp (propp(AT)math.wisc.edu)