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
Examples
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)
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
Crossrefs
Cf. A333236.
Programs
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PARI
See Links section.
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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
Formula
a(10*n) = a(n) + 1.
Comments