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A333442 For any n > 0, let Sum_{k >= 0} d_k / 10^k be the decimal representation of 1/n; a(n) is the least m such that d_m = max_{k >= 0} d_k.

%I A333442 #15 Feb 07 2022 21:46:29
%S A333442 0,1,1,2,1,2,4,3,1,1,2,2,4,6,2,2,9,2,10,2,6,3,12,4,2,3,3,8,15,2,15,5,
%T A333442 2,3,3,3,3,9,4,3,5,6,10,4,2,6,8,4,22,2,3,3,7,3,3,4,9,9,4,3,5,6,4,4,5,
%U A333442 3,4,13,5,5,35,4,5,4,3,8,4,4,6,4,9,5,8,4
%N A333442 For any n > 0, let Sum_{k >= 0} d_k / 10^k be the decimal representation of 1/n; a(n) is the least m such that d_m = max_{k >= 0} d_k.
%C A333442 In other words, a(n) is the position of the first occurrence of the largest digit in the decimal representation of 1/n (A333236).
%H A333442 Rémy Sigrist, <a href="/A333442/b333442.txt">Table of n, a(n) for n = 1..10000</a>
%H A333442 Rémy Sigrist, <a href="/A333442/a333442.gp.txt">PARI program for A333442</a>
%H A333442 <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>
%F A333442 a(10*n) = a(n) + 1.
%e A333442 The first terms, alongside 1/n with the first occurrence of A333236(n) in parentheses, are:
%e A333442   n   a(n)  1/n
%e A333442   --  ----  ---------------
%e A333442    1     0  (1)
%e A333442    2     1    0.(5)
%e A333442    3     1    0.(3)33333...
%e A333442    4     2    0.2(5)
%e A333442    5     1    0.(2)
%e A333442    6     2    0.1(6)6666...
%e A333442    7     4    0.142(8)57...
%e A333442    8     3    0.12(5)
%e A333442    9     1    0.(1)11111...
%e A333442   10     1    0.(1)
%o A333442 (PARI) See Links section.
%o A333442 (Python)
%o A333442 from sympy import n_order, multiplicity
%o A333442 def A333442(n):
%o A333442     if n == 1: return 0
%o A333442     m2, m5 = multiplicity(2,n), multiplicity(5,n)
%o A333442     r = max(m2,m5)+n_order(10,n//2**m2//5**m5)
%o A333442     s = str(10**r//n).zfill(r)
%o A333442     return s.index(max(s))+1 # _Chai Wah Wu_, Feb 07 2022
%Y A333442 Cf. A333236.
%K A333442 nonn,base
%O A333442 1,4
%A A333442 _Rémy Sigrist_, Mar 21 2020