OFFSET
1,2
COMMENTS
Apparently a(n)/3 mod 2 = A010060(n-1), the Thue-Morse sequence.
a(n+1) is the smallest number with exactly n+1 partitions into distinct powers of 2 or of 3: A131996(a(n+1)) = n+1 and A131996(m) < n+1 for m < a(n+1). - Reinhard Zumkeller, Aug 06 2007
LINKS
Sean A. Irvine, Table of n, a(n) for n = 1..1000
Ralf Stephan, Some divide-and-conquer sequences ...
Ralf Stephan, Table of generating functions
FORMULA
Apparently a(n) = 3*A005836(n).
G.f.: (x/(1 - x))*Sum_{k>=0} 3^(k+1)*x^(2^k)/(1 + x^(2^k)) (conjecture). - Ilya Gutkovskiy, Jul 23 2017
EXAMPLE
For n=0, A006134(0) = 1, hence 0 is a term.
MATHEMATICA
Select[Range[0, 1020], Mod[Sum[Binomial[2 k, k], {k, 0, #}], 3] != 0 &] (* Michael De Vlieger, Nov 28 2015 *)
PROG
(PARI) for(n=0, 1e3, if(sum(k=0, n, binomial(2*k, k)) % 3 > 0, print1(n, ", "))) \\ Altug Alkan, Nov 26 2015
(PARI) a(n)= fromdigits(binary(n-1), 3)*3 \\ Ruud H.G. van Tol, Jan 23 2026
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 22 2003
EXTENSIONS
Zero prepended to the sequence and formulas modified accordingly by L. Edson Jeffery, Nov 25 2015
STATUS
approved
