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

1,2

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

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

Crossrefs

Cf. A000108.

Sequence in context: A081467 A194119 A084721 * A274108 A368616 A138316

Adjacent sequences: A273038 A273039 A273040 * A273042 A273043 A273044

Keyword

nonn

Author

Jeffrey Shallit, May 13 2016

Status

approved