cp's OEIS Frontend

A273041 Discriminator of the Catalan numbers A000108.

%I A273041 #14 May 14 2016 13:43:54
%S A273041 1,2,5,5,11,11,16,16,23,23,23,23,47,47,64,64,64,64,71,71,141,141,141,
%T A273041 141,173,173,173,173,173,173,173,201,251,251,251,251,251,251,251,313,
%U A273041 313,313,383,383,383,383,383,519,519,519,519,519,519,519,519,519,601,601,601,601,601,601,601,601,601,601
%N A273041 Discriminator of the Catalan numbers A000108.
%C A273041 The discriminator of a sequence is the least positive integer k such that the first n terms of the sequence are pairwise distinct modulo k.
%H A273041 Robert Israel, <a href="/A273041/b273041.txt">Table of n, a(n) for n = 1..1127</a>
%p A273041 N = 100: # to get a(1) .. a(N)
%p A273041 F:= proc(m)
%p A273041   local G, i,j,x,S;
%p A273041   G:= 1+x; S:= {1};
%p A273041   for i from 2 do
%p A273041     G:= convert(series((x*G^2-1)/(2*x*G-1),x,2^i+1),polynom) mod m;
%p A273041     for j from 2^(i-1) to 2^i do
%p A273041       S:= S union {coeff(G,x,j)};
%p A273041       if nops(S) < j then return j-1 fi
%p A273041     od:
%p A273041   od
%p A273041 end proc:
%p A273041 nmax:= 1: A[1]:= 1:
%p A273041 for k from 2 while nmax < N do
%p A273041   v:= F(k);
%p A273041   if v > nmax then
%p A273041     for j from nmax+1 to v do A[j]:= k od:
%p A273041     nmax:= v;
%p A273041   fi:
%p A273041 od:
%p A273041 seq(A[i],i=1..N); # _Robert Israel_, May 13 2016
%Y A273041 Cf. A000108.
%K A273041 nonn
%O A273041 1,2
%A A273041 _Jeffrey Shallit_, May 13 2016