OFFSET
1,2
COMMENTS
Equivalently, members of A019469 divisible by 3, divided by 3.
Ralf Stephan's formula is that terms k written in ternary have an arbitrary least significant digit and above that only 0's and 1's (per A340051). - Kevin Ryde, May 22 2021
{3a(n)-1:n>=1} is the set of positive integers k such that the k-th central binomial coefficient is not divisible by (k+1)*(2k-1). Such integers k are characterized by the following property: k is congruent to 2 (mod 3), and at least one of k-1, k+1 has no 2's in its base-3 expansion. - Valerio De Angelis, Aug 08 2022
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..600
Kevin Ryde, Proof of Ralf Stephan's formula
Math Stackexchange, Factors of central binomial coefficient
FORMULA
a(n) = 9 * A005836(floor(n/6)) + (n mod 6) (conjectured) (confirmed, see links).
G.f.: x*(1+2*x)/(1-x^3) + 3/(1-x) * Sum_{i>=0} 3^i * x^(3*2^i) / (1 + x^(3*2^i)). - Kevin Ryde, May 22 2021
MATHEMATICA
Select[Range[300], Mod[(6#-4)!/((3#-2)!(3#-1)!), 3#]!=0&] (* Harvey P. Dale, Jun 11 2019 *)
PROG
(PARI) for(n=1, 300, if(((6*n-4)!/(3*n-2)!/(3*n-1)!)%(3*n), print1(n", ")))
(PARI) a(n) = my(r); [n, r]=divrem(n, 3); fromdigits(concat(binary(n), r), 3); \\ Kevin Ryde, May 22 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Aug 03 2004
STATUS
approved