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

%I A073078 #17 Mar 24 2024 02:49:31
%S A073078 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,
%T A073078 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,
%U A073078 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
%N A073078 Least k such that n divides C(2k,k).
%H A073078 Harvey P. Dale, <a href="/A073078/b073078.txt">Table of n, a(n) for n = 1..1000</a>
%F A073078 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).
%p A073078 A073078 := proc(n)
%p A073078     for k from 1 do
%p A073078         if modp(binomial(2*k,k),n) = 0 then
%p A073078             return k;
%p A073078         end if;
%p A073078     end do:
%p A073078 end proc: # _R. J. Mathar_, Aug 20 2014
%t A073078 lk[n_]:=Module[{k=1},While[!Divisible[Binomial[2k,k],n],k++];k]; Array[lk,90] (* _Harvey P. Dale_, Oct 09 2012 *)
%o A073078 (PARI) a(n)=if(n<0,0,s=1; while(binomial(2*s,s)%n>0,s++); s)
%Y A073078 Cf. A000984, A111869.
%K A073078 easy,nonn
%O A073078 1,3
%A A073078 _Benoit Cloitre_, Aug 17 2002