A175203 Numbers k that divide 10^(k+1)-1.

1, 3, 9, 11, 33, 77, 99, 143, 303, 369, 407, 707, 959, 1001, 1111, 2439, 2703, 2717, 2849, 3107, 3399, 3519, 4059, 4277, 5151, 5291, 6083, 6439, 6479, 8687, 9191, 9799, 9999, 10403, 10439, 10619, 11951, 12089, 13727, 13919, 16211, 18699, 22119, 24849

Offset

1,2

References

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 303, p. 76, Ellipses, Paris 2008.

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..250

Example

3 divides 10^4 - 1 = 3^2 * 11 * 101.
9 divides 10^10 - 1 = 3^2 * 11 * 41 * 271 * 9091.
11 divides 10^12 - 1 = 3^3 * 7 * 11 * 13 * 37 * 101 * 9901.
33 divides 10^34 - 1 = 3^2 * 11 * 103 * 4013 * 2071723 * 5363222357 * 21993833369.

Maple

with(numtheory):for n from 1 to 50000 do: x:= 10^(n+1) - 1: y:=irem(x, n): if y=0 then print (n):else fi:od:

Mathematica

Select[Flatten[10*#-{9, 7, 3, 1} & /@ Range@10000],
Mod[10^(1+#)-1, #]==0 &] (* Hans Rudolf Widmer, Oct 28 2023 *)

Prog

(PARI) isok(k) = Mod(10, k)^(k+1) == 1; \\ Michel Marcus, Jun 02 2024

Crossrefs

Cf. A002283.

Sequence in context: A200879 A027895 A027890 * A018282 A057245 A226477

Adjacent sequences: A175200 A175201 A175202 * A175204 A175205 A175206

Keyword

nonn

Author

Michel Lagneau, Mar 04 2010

Status

approved