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

Author

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

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A003592, A333236 (largest digit).

Programs

Mathematica

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

Formula

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

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

a(10^n) = 1.