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.

21, 38, 57, 58, 71, 81, 127, 148, 164, 181, 188, 195, 204, 208, 209, 212, 232, 244, 249, 250, 251, 252, 267, 269, 270, 300, 317, 326, 356, 357, 382, 398, 407, 409, 416, 417, 420, 447, 448, 453, 471, 479, 480, 481, 492, 502, 505, 528, 530, 548, 554, 561, 570

Offset

1,1

Comments

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.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

R. J. Mathar, Proof of alternative characterization.

Maple

Res:= NULL: count:= 0:
v:= 1:
for n from 2 while count < 100 do
  u:= floor((10/9)^n);
  if 9*u = 10*v then count:= count+1; Res:= Res, n-1 fi;
  v:= u;
od:
Res; # Robert Israel, Jul 10 2018

Mathematica

Select[Range[570], (Mod[10^(#+1), 9^(#+1)]/Mod[10^#, 9^#])==10&] (* James C. McMahon, Jul 05 2025 *)

Crossrefs

Cf. A139739, A065566.

Sequence in context: A061906 A385333 A380980 * A307278 A176071 A072708

Adjacent sequences: A139765 A139766 A139767 * A139769 A139770 A139771

Keyword

nonn

Author

Zak Seidov and N. J. A. Sloane, May 20 2008, May 24 2008

Status

approved