A019469 Numbers k such that k does not divide binomial(2*k-4, k-2).

2, 3, 4, 6, 8, 9, 12, 15, 16, 27, 30, 32, 33, 36, 39, 42, 64, 81, 84, 87, 90, 93, 96, 108, 111, 114, 117, 120, 123, 128, 243, 246, 249, 252, 255, 256, 258, 270, 273, 276, 279, 282, 285, 324, 327, 330, 333, 336, 339

Offset: 1

Author

Wouter Meeussen

Keywords

• nonn

Comments

Previous name was: Numbers n such that (n-2)-nd Catalan number is not divisible by n.

Conjecture (confirmed, see links): sequence is union of powers of two > 1 (A000079) and 3 * A096304.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Kevin Ryde, Proof of Wouter Meeussen's conjectured union

Crossrefs

Cf. A000079, A096304, A000984.

Complement of A019470.

Programs

Maple

A019469:=n->`if`(binomial(2*n-4,n-2) mod n <> 0,n,NULL): seq(A019469(n), n=1..400); # Wesley Ivan Hurt, Sep 13 2014

Mathematica

Select[Range[400],!Divisible[Binomial[2#-4,#-2],#]&] (* Harvey P. Dale, Aug 13 2015 *)

PARI

valp(n, p)=my(s); while(n\=p, s+=n); s
bin(n, p)=valp(2*n, p)-2*valp(n, p)
is(n)=my(f=factor(n)); for(i=1, #f~, if(bin(n-2, f[i, 1])Charles R Greathouse IV, Nov 04 2016

Extensions

Name changed by Wesley Ivan Hurt, Sep 16 2014