A347495 Factorial base Niven numbers (A118363) with a record gap to the next factorial base Niven number.

1, 2, 9, 12, 30, 40, 60, 192, 224, 318, 550, 640, 1136, 1989, 4875, 4980, 23355, 24272, 24378, 40131, 60192, 63872, 80472, 238680, 280140, 2027340, 2872620, 3622068, 13400475, 21293094, 25399080, 28584626, 111020840, 278690360, 355419734, 398884590, 834592590

Offset: 1

Author

Amiram Eldar, Sep 03 2021

Keywords

• nonn
• base

Comments

The corresponding gaps are 1, 2, 3, 4, 5, 8, 10, 12, 16, 18, 20, 32, 34, 39, 52, 55, 60, 67, 82, 85, 90, 96, 154, 174, 210, 216, 222, 268, 297, 318, 336, 346, 430, 466, 517, 546, 604, ...

Examples

			The first 8 factorial base Niven numbers are 1, 2, 4, 6, 8, 9, 12 and 16. The gaps between them are 1, 2, 2, 2, 1, 3 and 4. The record gaps, 1, 2, 3 and 4, occur after the terms 1, 2, 9 and 12.
		

Crossrefs

Cf. A034968, A118363, A328205, A337076, A337077, A347496.

Programs

Mathematica

fivenQ[n_] := Module[{s = 0, i = 2, k = n}, While[k > 0, k = Floor[n/i!]; s = s + (i - 1)*k; i++]; Divisible[n, n - s]]; gapmax = 0; n1 = 1; s = {}; Do[If[fivenQ[n], gap = n - n1; If[gap > gapmax, gapmax = gap; AppendTo[s, n1]]; n1 = n], {n, 2, 10^5}]; s (* after Jean-François Alcover at A034968 *)