A272881 Discriminator of the evil numbers (A001969).

1, 2, 4, 4, 7, 8, 8, 8, 13, 16, 16, 16, 16, 16, 16, 16, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 61, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 127, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128

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.

The discriminator of this sequence is given by 2^(i+1) - 3 if n = 2^i + 1 for odd i > 2; 2^(i+1) - 1 if n = 2^i + 1 for even i >= 2; and 2^(ceiling(log_2(n))) otherwise.

Links

Table of n, a(n) for n=1..83.

Arnold, L. K.; Benkoski, S. J.; and McCabe, B. J.; The discriminator (a simple application of Bertrand's postulate). Amer. Math. Monthly 92 (1985), 275-277.

Sajed Haque, Jeffrey Shallit, Discriminators and k-Regular Sequences, arXiv:1605.00092 [cs.DM], 2016.

Crossrefs

Cf. A001969.

Sequence in context: A164721 A194118 A266188 * A325646 A325723 A353927

Adjacent sequences: A272878 A272879 A272880 * A272882 A272883 A272884

Keyword

nonn

Author

Jeffrey Shallit, May 08 2016

Status

approved