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A369841
n-th digit of the decimal expansion of 1/n, with the digit to the left of the decimal point counted as the first digit.
1
1, 5, 3, 0, 0, 6, 7, 0, 1, 0, 9, 3, 3, 5, 6, 0, 7, 5, 1, 0, 4, 5, 3, 6, 0, 5, 3, 5, 1, 3, 9, 0, 3, 5, 5, 7, 7, 5, 2, 0, 9, 0, 3, 2, 2, 5, 7, 3, 8, 0, 1, 9, 3, 1, 1, 1, 1, 5, 1, 6, 9, 5, 1, 0, 3, 5, 7, 4, 1, 4, 9, 8, 3, 5, 3, 3, 9, 2, 1, 0, 7, 5, 3, 0, 7, 5, 1, 6, 1, 1, 9, 0, 1, 5, 5, 6, 7, 6, 1, 0
OFFSET
1,2
COMMENTS
The digits seem to occur with unequal frequency. In the limit as n increases, it seems that the digits, sorted in decreasing order of frequency of occurrence, are 0,5,1,3,7,9,2,6,8,4.
LINKS
FORMULA
a(n) = floor((10^(n-1))/n) mod 10.
EXAMPLE
a(2) = 5 since 1/2 = 0.5 and the 2nd digit of "0.5" (including the 0) is 5.
a(7) = 7 since 1/7 = 0.142857142857... and its 7th digit is 7.
From Jon E. Schoenfield, Feb 03 2024: (Start)
In each row of the following table, the n-th digit is surrounded by spaces:
.
n 1/n a(n)
-- ----------------- ----
1 1 .0000000000... 1
2 0. 5 000000000... 5
3 0.3 3 33333333... 3
4 0.25 0 0000000... 0
5 0.200 0 000000... 0
6 0.1666 6 66666... 6
7 0.14284 7 1428... 7
8 0.125000 0 000... 0
9 0.1111111 1 11... 1
10 0.10000000 0 0... 0
(End)
MATHEMATICA
Table[Mod[Floor[10^(n-1)/n], 10], {n, 100}] (* James C. McMahon, Feb 04 2024 *)
PROG
(Python)
def a(n): return (10**(n-1)//n)%10
print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Feb 03 2024
CROSSREFS
Cf. A061480.
Sequence in context: A046270 A139207 A137237 * A152419 A322758 A077602
KEYWORD
nonn,base
AUTHOR
Itamar Zamir, Feb 03 2024
STATUS
approved