A376088 Positive numbers k such that in the decimal expansion of 1/k a nonzero digit is never followed by a zero.

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

Author

Rémy Sigrist, Sep 09 2024

Keywords

• nonn
• base

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.

Examples

			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)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program
• Rémy Sigrist, C++ program
• Index entries for sequences related to decimal expansion of 1/n

Crossrefs

Cf. A003592, A052382, A060284.

Programs

PARI

\\ See Links section.
(C++) // See Links section.