A273041 Discriminator of the Catalan numbers A000108.

1, 2, 5, 5, 11, 11, 16, 16, 23, 23, 23, 23, 47, 47, 64, 64, 64, 64, 71, 71, 141, 141, 141, 141, 173, 173, 173, 173, 173, 173, 173, 201, 251, 251, 251, 251, 251, 251, 251, 313, 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

Offset: 1

Author

Jeffrey Shallit, May 13 2016

Keywords

• nonn

Comments

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.

Links

• Robert Israel, Table of n, a(n) for n = 1..1127

Crossrefs

Cf. A000108.

Programs

Maple

N = 100: # to get a(1) .. a(N)
F:= proc(m)
  local G, i,j,x,S;
  G:= 1+x; S:= {1};
  for i from 2 do
    G:= convert(series((x*G^2-1)/(2*x*G-1),x,2^i+1),polynom) mod m;
    for j from 2^(i-1) to 2^i do
      S:= S union {coeff(G,x,j)};
      if nops(S) < j then return j-1 fi
    od:
  od
end proc:
nmax:= 1: A[1]:= 1:
for k from 2 while nmax < N do
  v:= F(k);
  if v > nmax then
    for j from nmax+1 to v do A[j]:= k od:
    nmax:= v;
  fi:
od:
seq(A[i],i=1..N); # Robert Israel, May 13 2016