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%I #20 Jun 02 2024 08:19:16
%S 1,3,9,11,33,77,99,143,303,369,407,707,959,1001,1111,2439,2703,2717,
%T 2849,3107,3399,3519,4059,4277,5151,5291,6083,6439,6479,8687,9191,
%U 9799,9999,10403,10439,10619,11951,12089,13727,13919,16211,18699,22119,24849
%N Numbers k that divide 10^(k+1)-1.
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 303, p. 76, Ellipses, Paris 2008.
%H Hugo Pfoertner, <a href="/A175203/b175203.txt">Table of n, a(n) for n = 1..250</a>
%e 3 divides 10^4 - 1 = 3^2 * 11 * 101.
%e 9 divides 10^10 - 1 = 3^2 * 11 * 41 * 271 * 9091.
%e 11 divides 10^12 - 1 = 3^3 * 7 * 11 * 13 * 37 * 101 * 9901.
%e 33 divides 10^34 - 1 = 3^2 * 11 * 103 * 4013 * 2071723 * 5363222357 * 21993833369.
%p 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:
%t Select[Flatten[10*#-{9,7,3,1} & /@ Range@10000],
%t Mod[10^(1+#)-1,#]==0 &] (* _Hans Rudolf Widmer_, Oct 28 2023 *)
%o (PARI) isok(k) = Mod(10, k)^(k+1) == 1; \\ _Michel Marcus_, Jun 02 2024
%Y Cf. A002283.
%K nonn
%O 1,2
%A _Michel Lagneau_, Mar 04 2010