A272649 Compressed discriminator of the factorial numbers.

1, 2, 3, 7, 10, 13, 31, 37, 61, 83, 127, 179, 193, 277, 383, 479, 541, 641, 877, 1013, 1423, 2251, 2339, 2557, 2663, 3083, 3301, 5693, 6229, 9091, 9377, 17107, 25447, 31193, 39233, 40879, 46309, 61471, 72089, 81707, 86111, 91243, 116329, 136207, 149459, 163729

Offset

1,2

Comments

The discriminator of the factorials is A208494 (replacing a(1) with 1), and the compressed discriminator is defined by reducing blocks of equal/repeated terms to a single instance. Because the discriminator is a monotonically increasing sequence, the compressed discriminator is just the records transform of the discriminator. - R. J. Mathar, May 11 2016

References

Olivier Gérard, Posting to Sequence Fans Mailing List, May 08 2016.

Links

Table of n, a(n) for n=1..46.

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

Mathematica

R[n_, i_] := Union[Table[Mod[k!, i], {k, 1, n}]];
Reap[i0 = 1; Print[1]; Sow[1]; Do[Do[If[Length[R[n, i]] == n, If[i != i0, Print[i]; Sow[i]; i0 = i]; Goto[aa]], {i, 2, Max[n^2, 2]}]; Label[aa]; Continue, {n, 1, 10^4}] ][[2, 1]] (* Jean-François Alcover, Sep 14 2018, after Zhi-Wei Sun in A208494 *)

Crossrefs

Cf. A000142, A208494.

Sequence in context: A341238 A002238 A002255 * A266813 A344232 A370639

Adjacent sequences: A272646 A272647 A272648 * A272650 A272651 A272652

Keyword

nonn

Author

N. J. A. Sloane, May 10 2016

Extensions

a(32)-a(46) from Alois P. Heinz, May 11 2016

Status

approved