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%I #31 Oct 12 2024 09:02:19
%S 1,3,9,27,69,1053,1599,2511,8167,21371,73323,225681,313401,362703,
%T 371321,1896939,2735667,3426273,3795093,5433153,302278903,1371292077,
%U 19755637749,23560349643,33184178631
%N Numbers k such that the concatenation 1,2,3,...,(k-1) is divisible by k.
%C Subsequence of A029455 composed of the terms coprime to 10. - _Max Alekseyev_, Jun 07 2023
%C a(26) > 10^11. - _Jason Yuen_, Oct 12 2024
%e 3 divides 12, 9 divides 12345678.
%t s = ""; Do[s = s <> ToString[n]; If[Mod[ToExpression[s], n + 1] == 0, Print[n + 1]], {n, 0, 5*10^6}] (* _Ryan Propper_, Aug 28 2005 *)
%t Select[Range[55*10^5],Divisible[FromDigits[Flatten[IntegerDigits/@Range[ #-1]]],#]&] (* _Harvey P. Dale_, Mar 28 2020 *)
%o (Python) # See A029455 for concat_mod
%o def isok(k): return concat_mod(10, k-1, k)==0 # _Jason Yuen_, Oct 06 2024
%Y Cf. A007908, A029455, A094151, A171785, A332580, A362966.
%K base,nonn,more,hard
%O 1,2
%A _Amarnath Murthy_, Aug 10 2005
%E More terms from _Ryan Propper_, Aug 28 2005
%E a(20) from _Giovanni Resta_, Apr 10 2018
%E a(21)-a(24) from _Scott R. Shannon_, using a modified version of an algorithm by _Joseph Myers_, Apr 10 2020
%E a(25) from _Jason Yuen_, Oct 06 2024