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A110740
Numbers k such that the concatenation 1,2,3,...,(k-1) is divisible by k.
5
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
1,2
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
EXAMPLE
3 divides 12, 9 divides 12345678.
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 *)
PROG
(Python) # See A029455 for concat_mod
def isok(k): return concat_mod(10, k-1, k)==0 # Jason Yuen, Oct 06 2024
CROSSREFS
KEYWORD
base,nonn,more,hard
AUTHOR
Amarnath Murthy, Aug 10 2005
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
STATUS
approved