A273098 Discriminator of first half of row n of Pascal's triangle.

1, 1, 2, 3, 4, 6, 4, 8, 13, 11, 13, 8, 17, 20, 12, 16, 23, 19, 35, 28, 41, 23, 41, 20, 37, 53, 47, 29, 61, 31, 76, 32, 63, 67, 61, 37, 101, 73, 131, 41, 101, 43, 67, 108, 83, 47, 119, 70, 137, 61, 118, 53, 127, 113, 137, 128, 167, 59, 179, 61, 173, 202, 206, 64, 239, 67, 334, 278, 213, 71, 179, 73, 185, 386, 269, 218, 277, 79, 197, 283

Offset: 0

Author

Jeffrey Shallit, May 15 2016

Keywords

• nonn

Comments

The discriminator of a finite sequence is the least positive integer k such that all of its terms are pairwise incongruent, modulo k. Here the n-th term of the sequence is the discriminator of binomial(n, 0), binomial(n,1), ..., binomial(n,t) where t = floor(n/2).

It appears that a(2^k-1) = 2^k for k >= 3. - Robert Israel, May 15 2016

Links

• Robert Israel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A007318, A034868.

Programs

Maple

discriminator:= proc(L)
  local n,k;
  n:= nops(L);
  for k from n do if nops (L mod k) =n  then return k fi od:
end proc;
seq(discriminator({seq(binomial(n,j),j=0..floor(n/2))}),n=0..100); # Robert Israel, May 15 2016