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A096304 Numbers k such that 3k does not divide (6k-4)!/((3k-2)!*(3k-1)!). 5
1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 27, 28, 29, 30, 31, 32, 36, 37, 38, 39, 40, 41, 81, 82, 83, 84, 85, 86, 90, 91, 92, 93, 94, 95, 108, 109, 110, 111, 112, 113, 117, 118, 119, 120, 121, 122, 243, 244, 245, 246, 247, 248, 252, 253, 254, 255, 256, 257, 270, 271 (list; graph; refs; listen; history; text; internal format)
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 (as per A340051). - Kevin Ryde, May 22 2021

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..600

Kevin Ryde, Proof of Ralf Stephan's formula

Index entries for 3-automatic sequences.

FORMULA

a(n) = 9 * A005836([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

Cf. A340051 (ternary digits), A005836, A019469, A187358.

Sequence in context: A068586 A068585 A037472 * A119955 A158573 A194398

Adjacent sequences:  A096301 A096302 A096303 * A096305 A096306 A096307

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Aug 03 2004

STATUS

approved

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Last modified July 25 02:56 EDT 2021. Contains 346282 sequences. (Running on oeis4.)