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

1,2

Comments

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

Links

Table of n, a(n) for n=1..52.

Example

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

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 *)

Crossrefs

Cf. A160818.

Sequence in context: A227001 A248954 A082937 * A160818 A244514 A082810

Adjacent sequences: A214016 A214017 A214018 * A214020 A214021 A214022

Keyword

base,nonn

Author

Arkadiusz Wesolowski, Jul 01 2012

Status

approved