A216664 - OEIS

%I #23 Mar 04 2022 15:11:45

%S 11,17,19,23,29,47,59,61,73,91,95,97,101,103,109,113,127,131,137,139,

%T 149,167,179,181,189,193,211,223,229,233,251,255,257,263,269,313,325,

%U 331,337,349,353,367,379,383,389,419,421,433,441,457,461,463,477,487,491

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

%C First nine terms are primes.

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

%H Arkadiusz Wesolowski, <a href="/A216664/b216664.txt">Table of n, a(n) for n = 1..1000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Midy%27s_theorem">Midy's theorem</a>

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

%e 1/17 = .058823529..., therefore 17 is a term.

%e 1/21 = .04761904761..., therefore 21 is not a term.

%t 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

%o (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

%o (Python)

%o from itertools import count, islice

%o def A216664_gen(startvalue=1): # generator of terms >= startvalue

%o     for n in count(max(startvalue+1-startvalue%2,1),2):

%o         if 10**((n+1)//2)//n % 10 == 9:

%o             yield n

%o A216664_list = list(islice(A216664_gen(),20)) # _Chai Wah Wu_, Mar 04 2022

%Y Cf. A187040.

%K base,nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Sep 14 2012