A214019 a(n) is the smallest positive number such that n divides the sum of all numbers formed by cyclically permuting digits of a(n).

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 370, 407, 444, 481, 518, 555, 592, 629, 666, 777, 888, 999, 1111, 1818, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999

Offset: 1

Author

Arkadiusz Wesolowski, Jul 01 2012

Keywords

• base
• nonn

Comments

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

Examples

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

Crossrefs

Cf. A160818.

Programs

Mathematica

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 *)