cp's OEIS Frontend

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

%I A273098 #20 Nov 03 2019 19:46:44
%S A273098 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,
%T A273098 47,29,61,31,76,32,63,67,61,37,101,73,131,41,101,43,67,108,83,47,119,
%U A273098 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
%N A273098 Discriminator of first half of row n of Pascal's triangle.
%C A273098 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).
%C A273098 It appears that a(2^k-1) = 2^k for k >= 3. - _Robert Israel_, May 15 2016
%H A273098 Robert Israel, <a href="/A273098/b273098.txt">Table of n, a(n) for n = 0..1000</a>
%p A273098 discriminator:= proc(L)
%p A273098   local n,k;
%p A273098   n:= nops(L);
%p A273098   for k from n do if nops (L mod k) =n  then return k fi od:
%p A273098 end proc;
%p A273098 seq(discriminator({seq(binomial(n,j),j=0..floor(n/2))}),n=0..100); # _Robert Israel_, May 15 2016
%Y A273098 Cf. A007318, A034868.
%K A273098 nonn
%O A273098 0,3
%A A273098 _Jeffrey Shallit_, May 15 2016