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A352153
Smallest digit in the decimal expansion of 1/n, ignoring leading and trailing 0's.
8
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.
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
KEYWORD
nonn,base
AUTHOR
STATUS
approved