A216664 Odd numbers n such that the decimal expansion of 1/n contains the digit "9" at position (n + 1)/2.

11, 17, 19, 23, 29, 47, 59, 61, 73, 91, 95, 97, 101, 103, 109, 113, 127, 131, 137, 139, 149, 167, 179, 181, 189, 193, 211, 223, 229, 233, 251, 255, 257, 263, 269, 313, 325, 331, 337, 349, 353, 367, 379, 383, 389, 419, 421, 433, 441, 457, 461, 463, 477, 487, 491

Offset

1,1

Comments

First nine terms are primes.

This is not a subsequence of A187040: 189 belongs to this sequence but not to A187040.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000

Wikipedia, Midy's theorem

Index entries for sequences related to decimal expansion of 1/n

Example

1/17 = .058823529..., therefore 17 is a term.
1/21 = .04761904761..., therefore 21 is not a term.

Mathematica

lst = {}; Do[l = (n + 1)/2; d = Flatten@RealDigits[1/n, 10, l]; If[Join[Table[0, {-1*Last@d}], Most@d][[l]] == 9, AppendTo[lst, n]], {n, 1, 491, 2}]; lst

Prog

(PARI) forstep(n=1, 491, 2, s=(n+1)/2; "\p s"; if(Mod(floor(10^s/n), 10)==9, print1(n, ", "))); \\ Arkadiusz Wesolowski, Aug 23 2013
(Python)
from itertools import count, islice
def A216664_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue+1-startvalue%2, 1), 2):
        if 10**((n+1)//2)//n % 10 == 9:
            yield n
A216664_list = list(islice(A216664_gen(), 20)) # Chai Wah Wu, Mar 04 2022

Crossrefs

Cf. A187040.

Sequence in context: A050778 A316100 A049593 * A019412 A178641 A226682

Adjacent sequences: A216661 A216662 A216663 * A216665 A216666 A216667

Keyword

base,nonn

Author

Arkadiusz Wesolowski, Sep 14 2012

Status

approved