cp's OEIS Frontend

A381578 For n > 0, for k > n, a(n) is the least k such that the pre-period and first period of the decimal expansion of n/k contains every digit of n at least as many times it is contained in n.

%I A381578 #14 Mar 02 2025 23:21:30
%S A381578 6,7,8,7,7,9,8,9,10,17,17,14,17,17,17,17,19,19,21,21,23,23,29,28,27,
%T A381578 27,28,29,32,31,34,34,38,38,38,38,38,39,46,43,42,43,46,46,46,47,49,49,
%U A381578 51,51,53,53,57,56,57,57,58,59,61,61,62,63,65,65,68,67,68,69
%N A381578 For n > 0, for k > n, a(n) is the least k such that the pre-period and first period of the decimal expansion of n/k contains every digit of n at least as many times it is contained in n.
%C A381578 What is the density of a(n) = prime in this sequence ?
%e A381578 n = 1:
%e A381578   1/2 = 0.500...
%e A381578   1/3 = 0.33...
%e A381578   1/4 = 0.2500...
%e A381578   1/5 = 0.200...
%e A381578   1/6 = 0.166... contains the digit 1, thus a(1) = 6.
%e A381578 n = 2:
%e A381578   2/3 = 0.66...
%e A381578   2/4 = 0.500...
%e A381578   2/5 = 0.400...
%e A381578   2/6 = 0.33...
%e A381578   2/7 = 0.285714285714...contains the digit 2, thus a(2) = 7.
%t A381578 a[n_] := Module[{k = n+1, r = Range[0, 9]}, While[! AllTrue[Count[Flatten[RealDigits[n/k][[1]]], #] & /@ r - DigitCount[n, 10, r], # >= 0 &], k++]; k]; Array[a, 100] (* _Amiram Eldar_, Feb 28 2025 *)
%Y A381578 Cf. A002371, A007732.
%K A381578 nonn,base
%O A381578 1,1
%A A381578 _Ctibor O. Zizka_, Feb 28 2025