A073078 Least k such that n divides C(2k,k).

1, 1, 2, 3, 3, 2, 4, 7, 5, 3, 6, 5, 7, 4, 8, 15, 9, 5, 10, 3, 5, 6, 12, 7, 13, 7, 14, 5, 15, 8, 16, 31, 6, 9, 4, 5, 19, 10, 7, 13, 21, 5, 22, 6, 8, 12, 24, 15, 25, 13, 11, 7, 27, 14, 8, 11, 11, 15, 30, 14, 31, 16, 5, 63, 8, 6, 34, 9, 14, 4, 36, 14, 37, 19, 14, 10, 6, 7, 40, 15, 41, 21

Offset: 1

Author

Benoit Cloitre, Aug 17 2002

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000984, A111869.

Programs

Maple

A073078 := proc(n)
    for k from 1 do
        if modp(binomial(2*k,k),n) = 0 then
            return k;
        end if;
    end do:
end proc: # R. J. Mathar, Aug 20 2014

Mathematica

lk[n_]:=Module[{k=1},While[!Divisible[Binomial[2k,k],n],k++];k]; Array[lk,90] (* Harvey P. Dale, Oct 09 2012 *)

PARI

a(n)=if(n<0,0,s=1; while(binomial(2*s,s)%n>0,s++); s)

Formula

a(2^k)=2^k-1, if n is an odd prime a(n)=(n+1)/2 (but there are also some composites satisfying this property, see A079290).