A110740 Numbers k such that the concatenation 1,2,3,...,(k-1) is divisible by k.

1, 3, 9, 27, 69, 1053, 1599, 2511, 8167, 21371, 73323, 225681, 313401, 362703, 371321, 1896939, 2735667, 3426273, 3795093, 5433153, 302278903, 1371292077, 19755637749, 23560349643, 33184178631

Offset: 1

Author

Amarnath Murthy, Aug 10 2005

Keywords

• base
• nonn
• more
• hard

Comments

Subsequence of A029455 composed of the terms coprime to 10. - Max Alekseyev, Jun 07 2023

a(26) > 10^11. - Jason Yuen, Oct 12 2024

Examples

			3 divides 12, 9 divides 12345678.
		

Crossrefs

Cf. A007908, A029455, A094151, A171785, A332580, A362966.

Programs

Mathematica

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 *)
Select[Range[55*10^5],Divisible[FromDigits[Flatten[IntegerDigits/@Range[ #-1]]],#]&] (* Harvey P. Dale, Mar 28 2020 *)

Python

# See A029455 for concat_mod
def isok(k): return concat_mod(10, k-1, k)==0 # Jason Yuen, Oct 06 2024

Extensions

More terms from Ryan Propper, Aug 28 2005

a(20) from Giovanni Resta, Apr 10 2018

a(21)-a(24) from Scott R. Shannon, using a modified version of an algorithm by Joseph Myers, Apr 10 2020

a(25) from Jason Yuen, Oct 06 2024