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

1,2

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, ...

Links

Table of n, a(n) for n=1..35.

Example

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.

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

Crossrefs

Cf. A333426, A333427, A337076, A337077, A347495.

Sequence in context: A053900 A318681 A183207 * A304797 A337360 A340038

Adjacent sequences: A347493 A347494 A347495 * A347497 A347498 A347499

Keyword

nonn,base

Author

Amiram Eldar, Sep 03 2021

Status

approved