The On-Line Encyclopedia of Integer Sequences (OEIS)

A352155 revision #8

A352155

Numbers m such that the smallest digit in the decimal expansion of 1/m is 1, ignoring leading and trailing 0's.

1, 6, 7, 8, 9, 10, 14, 24, 26, 28, 32, 35, 54, 55, 56, 60, 64, 65, 66, 70, 72, 74, 75, 80, 82, 88, 90, 100, 104, 112, 128, 140, 175, 176, 224, 240, 260, 280, 320, 350, 432, 448, 468, 504, 512, 528, 540, 548, 550, 560, 572, 576, 584, 592, 600, 616, 625, 640, 650, 660

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Leading 0's are not considered, otherwise every integer >= 11 would be a term (see examples).

Trailing 0's are also not considered, otherwise numbers of the form 2^i*5^j with i, j >= 0, apart from 1 (A003592) would be terms.

If k is a term, 10*k is also a term; so, terms with no trailing zeros are all primitive terms.

{8, 88, 888, ...} = A002282 \ {0} is a subsequence.

LINKS

Table of n, a(n) for n=1..60.

FORMULA

A352153(a(n)) = 1.

EXAMPLE

m = 14 is a term since 1/14 = 0.0714285714285714285... and the smallest term after the leading 0 is 1.

m = 240 is a term since 1/240 = 0.00416666666... and the smallest term after the leading 0's is 1.

m = 888 is a term since 1/888 = 0.001126126126... and the smallest term after the leading 0's is 1.

MATHEMATICA

f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 1100, Min@ f@# == 1 &]

CROSSREFS

Cf. A002282, A333402, A352153.

Similar with smallest digit k: A352154 (k=0), this sequence (k=1), A352156 (k=2), A352157 (k=3), A352158 (k=4), A352159 (k=5), A352160 (k=6), A352161 (k=7).

Sequence in context: A115840 A371565 A353437 * A058368 A321852 A108613

Adjacent sequences: A352152 A352153 A352154 * A352156 A352157 A352158

KEYWORD

nonn,base

AUTHOR

Bernard Schott and Robert G. Wilson v, Mar 17 2022

STATUS

proposed