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

Author

Jeffrey Shallit, May 08 2016

Keywords

• nonn

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

• 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.