A333442 - OEIS

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 #15 Feb 07 2022 21:46:29

%S 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 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 3,4,13,5,5,35,4,5,4,3,8,4,4,6,4,9,5,8,4

%N 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 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 Rémy Sigrist, <a href="/A333442/b333442.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A333442/a333442.gp.txt">PARI program for A333442</a>

%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>

%F a(10*n) = a(n) + 1.

%e The first terms, alongside 1/n with the first occurrence of A333236(n) in parentheses, are:

%e n a(n) 1/n

%e -- ---- ---------------

%e 1 0 (1)

%e 2 1 0.(5)

%e 3 1 0.(3)33333...

%e 4 2 0.2(5)

%e 5 1 0.(2)

%e 6 2 0.1(6)6666...

%e 7 4 0.142(8)57...

%e 8 3 0.12(5)

%e 9 1 0.(1)11111...

%e 10 1 0.(1)

%o (PARI) See Links section.

%o (Python)

%o from sympy import n_order, multiplicity

%o def A333442(n):

%o if n == 1: return 0

%o m2, m5 = multiplicity(2,n), multiplicity(5,n)

%o r = max(m2,m5)+n_order(10,n//2**m2//5**m5)

%o s = str(10**r//n).zfill(r)

%o return s.index(max(s))+1 # _Chai Wah Wu_, Feb 07 2022

%Y Cf. A333236.

%K nonn,base

%O 1,4

%A _Rémy Sigrist_, Mar 21 2020