A352153 Smallest digit in the decimal expansion of 1/n, ignoring leading and trailing 0's.

1, 5, 3, 2, 2, 1, 1, 1, 1, 1, 0, 3, 0, 1, 6, 2, 0, 5, 0, 5, 0, 4, 0, 1, 4, 1, 0, 1, 0, 3, 0, 1, 0, 0, 1, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0

Offset

1,2

Comments

Leading 0's are not considered, otherwise a(n) would be 0 when n >= 11 (see examples for 13 and 14).

Trailing 0's are not also considered, otherwise when 1/n is a terminating decimal (A003592), a(n) would be also 0.

Links

Table of n, a(n) for n=1..94.

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

Formula

a(n) = n iff n = 1 or n = 3.

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

a(10^n) = 1.

Example

1/13 = 0.076923076923076923... with periodic part = '769230' (or '076923'), hence a(13) = 0.
1/14 = 0.0714285714285714285... with periodic part = '714285', hence a(14) = 1.
1/40 = 0.025 hence a(40) = 2.

Mathematica

f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Array[Min@ f@# &, 105]

Crossrefs

Cf. A003592, A333236 (largest digit).

Sequence in context: A201333 A353179 A088324 * A052038 A278647 A249802

Adjacent sequences: A352150 A352151 A352152 * A352154 A352155 A352156

Keyword

nonn,base

Author

Bernard Schott and Robert G. Wilson v, Mar 06 2022

Status

approved