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A139768 Numbers k such that (10^(k+1) mod 9^(k+1))/(10^k mod 9^k)=10, or A139739(k+1)/A139739(k)=10.

%I A139768 #12 Jul 05 2025 14:44:06
%S A139768 21,38,57,58,71,81,127,148,164,181,188,195,204,208,209,212,232,244,
%T A139768 249,250,251,252,267,269,270,300,317,326,356,357,382,398,407,409,416,
%U A139768 417,420,447,448,453,471,479,480,481,492,502,505,528,530,548,554,561,570
%N A139768 Numbers k such that (10^(k+1) mod 9^(k+1))/(10^k mod 9^k)=10, or A139739(k+1)/A139739(k)=10.
%C A139768 Also, this is the set of numbers k such that 9*floor((10/9)^(k+1))==10*floor((10/9)^k) (cf. A065566). For proof see Mathar link.
%H A139768 Robert Israel, <a href="/A139768/b139768.txt">Table of n, a(n) for n = 1..10000</a>
%H A139768 R. J. Mathar, <a href="/A139768/a139768.txt">Proof of alternative characterization.</a>
%p A139768 Res:= NULL: count:= 0:
%p A139768 v:= 1:
%p A139768 for n from 2 while count < 100 do
%p A139768   u:= floor((10/9)^n);
%p A139768   if 9*u = 10*v then count:= count+1; Res:= Res, n-1 fi;
%p A139768   v:= u;
%p A139768 od:
%p A139768 Res; # _Robert Israel_, Jul 10 2018
%t A139768 Select[Range[570],(Mod[10^(#+1),9^(#+1)]/Mod[10^#,9^#])==10&] (* _James C. McMahon_, Jul 05 2025 *)
%Y A139768 Cf. A139739, A065566.
%K A139768 nonn
%O A139768 1,1
%A A139768 _Zak Seidov_ and _N. J. A. Sloane_, May 20 2008, May 24 2008