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

Author

Arkadiusz Wesolowski, Sep 14 2012

Keywords

• base
• nonn

Comments

First nine terms are primes.

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

Examples

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

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

Crossrefs

Cf. A187040.

Programs

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

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