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

%I #12 Sep 14 2024 06:46:22

%S 3,6,7,9,12,14,15,18,22,24,26,28,30,35,36,44,45,54,55,56,60,65,66,70,

%T 72,74,75,82,88,90,104,108,112,120,132,140,144,148,150,175,176,180,

%U 216,220,224,225,240,252,260,264,275,280,288,292,296,300,308,350,360

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

%C Or numbers k such that 1/k has only one (infinite) run of (leading) zeros.

%C 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).

%C This sequence is infinite: if m is a term, then 10*m is also a term.

%H Rémy Sigrist, <a href="/A376088/b376088.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A376088/a376088.gp.txt">PARI program</a>

%H Rémy Sigrist, <a href="/A376088/a376088.txt">C++ program</a>

%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>

%e The first terms, alongside their reciprocal (with the repeating part between parentheses), are:

%e n a(n) 1/a(n)

%e -- ---- ------------

%e 1 3 0.(3)

%e 2 6 0.1(6)

%e 3 7 0.(142857)

%e 4 9 0.(1)

%e 5 12 0.08(3)

%e 6 14 0.0(714285)

%e 7 15 0.0(6)

%e 8 18 0.0(5)

%e 9 22 0.0(45)

%e 10 24 0.041(6)

%e 11 26 0.0(384615)

%e 12 28 0.03(571428)

%e 13 30 0.0(3)

%e 14 35 0.0(285714)

%e 15 36 0.02(7)

%o (PARI) \\ See Links section.

%o (C++) // See Links section.

%Y Cf. A003592, A052382, A060284.

%K nonn,base

%O 1,1

%A _Rémy Sigrist_, Sep 09 2024