|
%I #20 Feb 23 2024 21:40:08
%S 1,2,10,22,25,29,33,70,118,358,598,1438,1803,1819,2878,2881,2997,4318,
%T 4322,4388,10078,20158,21967,21971,21975,30238,30241,30837,40318,
%U 120958,141121,142557,201598,214563,214675,282238,362878,649446,649504,1088638,1303204,1303314
%N Numbers k such that k divides the sum of digits in factorial base of all numbers from 1 to k.
%C The corresponding quotients are 1, 1, 2, 3, 3, 3, 3, 4, 5, ...
%H Amiram Eldar, <a href="/A333702/b333702.txt">Table of n, a(n) for n = 1..137</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%e 10 is a term since the sum of digits in factorial base (A034968) of k from 1 to 10 is 1 + 1 + 2 + 2 + 3 + 1 + 2 + 2 + 3 + 3 = 20, which is divisible by 10.
%t f[n_] := Module[{s=0, i=2, k=n}, While[k > 0, k = Floor[n/i!]; s = s + (i-1)*k; i++]; n-s]; seq = {}; s = 0; Do[s += f[n]; If[Divisible[s, n], AppendTo[seq, n]], {n, 1, 10^5}]; seq (* after _Jean-François Alcover_ at A034968 *)
%Y Cf. A007623, A034968, A368342.
%Y Cf. A095376, A114136, A333703, A333704, A333705.
%K nonn,base
%O 1,2
%A _Amiram Eldar_, Apr 02 2020
|
