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.

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

Offset

1,4

Comments

In other words, a(n) is the position of the first occurrence of the largest digit in the decimal representation of 1/n (A333236).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A333442

Index entries for sequences related to decimal expansion of 1/n

Formula

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

Example

The first terms, alongside 1/n with the first occurrence of A333236(n) in parentheses, are:
  n   a(n)  1/n
  --  ----  ---------------
   1     0  (1)
   2     1    0.(5)
   3     1    0.(3)33333...
   4     2    0.2(5)
   5     1    0.(2)
   6     2    0.1(6)6666...
   7     4    0.142(8)57...
   8     3    0.12(5)
   9     1    0.(1)11111...
  10     1    0.(1)

Prog

(PARI) See Links section.
(Python)
from sympy import n_order, multiplicity
def A333442(n):
    if n == 1: return 0
    m2, m5 = multiplicity(2, n), multiplicity(5, n)
    r = max(m2, m5)+n_order(10, n//2**m2//5**m5)
    s = str(10**r//n).zfill(r)
    return s.index(max(s))+1 # Chai Wah Wu, Feb 07 2022

Crossrefs

Cf. A333236.

Sequence in context: A181293 A262876 A263045 * A319563 A201912 A201908

Adjacent sequences: A333439 A333440 A333441 * A333443 A333444 A333445

Keyword

nonn,base

Author

Rémy Sigrist, Mar 21 2020

Status

approved