A347496 Primorial base Niven numbers (A333426) with a record gap to the next primorial base Niven number.

1, 2, 9, 12, 25, 50, 120, 344, 400, 770, 1120, 3920, 13566, 13734, 19845, 22748, 148148, 167854, 176220, 889896, 2946216, 3685416, 5072256, 7139280, 8521056, 9058900, 9625336, 17825857, 19392072, 27504848, 76952788, 106691001, 162789696, 198582784, 212847225

Offset: 1

Author

Amiram Eldar, Sep 03 2021

Keywords

• nonn
• base

Comments

The corresponding gaps are 1, 2, 3, 4, 5, 10, 12, 16, 20, 34, 37, 48, 54, 66, 75, 121, 132, 146, 180, 238, 241, 248, 288, 302, 314, 332, 336, 343, 348, 400, 476, 479, 484, 496, 500, ...

Examples

			The first 8 primorial 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. A333426, A333427, A337076, A337077, A347495.

Programs

Mathematica

max = 7; bases = Prime @ Range[max, 1, -1]; nmax = Times @@ bases - 1; sumdig[n_] := Plus @@ IntegerDigits[n, MixedRadix[bases]]; primoNivenQ[n_] := Divisible[n, sumdig[n]]; gapmax = 0; n1 = 1; s = {}; Do[If[primoNivenQ[n], gap = n - n1; If[gap > gapmax, gapmax = gap; AppendTo[s, n1]]; n1 = n], {n, 2, nmax}]; s