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A376088
Positive numbers k such that in the decimal expansion of 1/k a nonzero digit is never followed by a zero.
1
3, 6, 7, 9, 12, 14, 15, 18, 22, 24, 26, 28, 30, 35, 36, 44, 45, 54, 55, 56, 60, 65, 66, 70, 72, 74, 75, 82, 88, 90, 104, 108, 112, 120, 132, 140, 144, 148, 150, 175, 176, 180, 216, 220, 224, 225, 240, 252, 260, 264, 275, 280, 288, 292, 296, 300, 308, 350, 360
OFFSET
1,1
COMMENTS
Or numbers k such that 1/k has only one (infinite) run of (leading) zeros.
Or numbers k such that 1/k has only one infinite run of nonzero digits (considering that reciprocals of terms of A003592 end with 0's).
This sequence is infinite: if m is a term, then 10*m is also a term.
EXAMPLE
The first terms, alongside their reciprocal (with the repeating part between parentheses), are:
n a(n) 1/a(n)
-- ---- ------------
1 3 0.(3)
2 6 0.1(6)
3 7 0.(142857)
4 9 0.(1)
5 12 0.08(3)
6 14 0.0(714285)
7 15 0.0(6)
8 18 0.0(5)
9 22 0.0(45)
10 24 0.041(6)
11 26 0.0(384615)
12 28 0.03(571428)
13 30 0.0(3)
14 35 0.0(285714)
15 36 0.02(7)
PROG
(PARI) \\ See Links section.
(C++) // See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Sep 09 2024
STATUS
approved