A208494 -id:A208494 - cp's OEIS frontend

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

N. J. A. Sloane, May 10 2016

nonn

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

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

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.

Cf. A000142, A208494.

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 *)

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

cp's OEIS Frontend

A272649 Compressed discriminator of the factorial numbers.

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