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A273098
Discriminator of first half of row n of Pascal's triangle.
1
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
0,3
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
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
CROSSREFS
Sequence in context: A049044 A366577 A102284 * A328166 A266447 A100700
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, May 15 2016
STATUS
approved