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%I #7 Sep 03 2021 20:56:57
%S 1,2,9,12,25,50,120,344,400,770,1120,3920,13566,13734,19845,22748,
%T 148148,167854,176220,889896,2946216,3685416,5072256,7139280,8521056,
%U 9058900,9625336,17825857,19392072,27504848,76952788,106691001,162789696,198582784,212847225
%N Primorial base Niven numbers (A333426) with a record gap to the next primorial base Niven number.
%C 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, ...
%e 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.
%t 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
%Y Cf. A333426, A333427, A337076, A337077, A347495.
%K nonn,base
%O 1,2
%A _Amiram Eldar_, Sep 03 2021
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