A214019 - OEIS

%I #19 Mar 01 2024 02:05:06

%S 1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,111,222,333,370,407,444,

%T 481,518,555,592,629,666,777,888,999,1111,1818,2222,3333,4444,5555,

%U 6666,7777,8888,9999,11111,22222,33333,44444,55555,66666,77777,88888,99999

%N a(n) is the smallest positive number such that n divides the sum of all numbers formed by cyclically permuting digits of a(n).

%C Many terms in this sequence are the same as A160818(n) but not all.

%e For example with 481: 481 + 814 + 148 = 1443 and 481 divides 1443.

%t lst = {}; cycDigitPerms[n_Integer, b_: 10] := Module[{list = {n}, digits = IntegerDigits[n, b], len, counter, holder, next}, len = Length[digits]; counter = 1; While[counter < len, holder = digits[[-1]]; digits = Drop[digits, -1]; digits = Insert[digits, holder, 1]; list = Append[list, FromDigits[digits, b]]; counter++]; Return[list]]; Do[If[Divisible[Total@cycDigitPerms[n], n], AppendTo[lst, n]], {n, 10^5}]; lst (* Most of the code is from _Alonso del Arte_ *)

%Y Cf. A160818.

%K base,nonn

%O 1,2

%A _Arkadiusz Wesolowski_, Jul 01 2012