A273041 - OEIS

%I #14 May 14 2016 13:43:54

%S 1,2,5,5,11,11,16,16,23,23,23,23,47,47,64,64,64,64,71,71,141,141,141,

%T 141,173,173,173,173,173,173,173,201,251,251,251,251,251,251,251,313,

%U 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 Discriminator of the Catalan numbers A000108.

%C 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 Robert Israel, <a href="/A273041/b273041.txt">Table of n, a(n) for n = 1..1127</a>

%p N = 100: # to get a(1) .. a(N)

%p F:= proc(m)

%p   local G, i,j,x,S;

%p   G:= 1+x; S:= {1};

%p   for i from 2 do

%p     G:= convert(series((x*G^2-1)/(2*x*G-1),x,2^i+1),polynom) mod m;

%p     for j from 2^(i-1) to 2^i do

%p       S:= S union {coeff(G,x,j)};

%p       if nops(S) < j then return j-1 fi

%p     od:

%p   od

%p end proc:

%p nmax:= 1: A[1]:= 1:

%p for k from 2 while nmax < N do

%p   v:= F(k);

%p   if v > nmax then

%p     for j from nmax+1 to v do A[j]:= k od:

%p     nmax:= v;

%p   fi:

%p od:

%p seq(A[i],i=1..N); # _Robert Israel_, May 13 2016

%Y Cf. A000108.

%K nonn

%O 1,2

%A _Jeffrey Shallit_, May 13 2016