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

1,3

Links

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

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).

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 *)

Prog

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

Crossrefs

Cf. A000984, A111869.

Sequence in context: A131469 A309076 A343326 * A360296 A034799 A008985

Adjacent sequences: A073075 A073076 A073077 * A073079 A073080 A073081

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 17 2002

Status

approved