A175688 Numbers k with property that arithmetic mean of its digits is both an integer and one of the digits of k.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 102, 111, 120, 123, 132, 135, 147, 153, 159, 174, 195, 201, 204, 210, 213, 222, 231, 234, 240, 243, 246, 258, 264, 285, 306, 312, 315, 321, 324, 333, 342, 345, 351, 354, 357, 360, 369, 375, 396, 402

Offset

1,3

Comments

Subsequence of A061383.

A180160(a(n)) = 0. - Reinhard Zumkeller, Aug 15 2010

Links

R. Zumkeller, Table of n, a(n) for n = 1..10000

Example

135 is in the list because (1+3+5)/3 = 3 and 3 is a digit of 135.

Mathematica

idQ[n_]:=Module[{idn=IntegerDigits[n], m}, m=Mean[idn]; IntegerQ[m] && MemberQ[idn, m]]; Select[Range[0, 500], idQ] (* Harvey P. Dale, Jun 10 2011 *)

Prog

(Haskell)
a175688 n = a175688_list !! (n-1)
a175688_list = filter f [0..] where
   f x = m == 0 && ("0123456789" !! avg) `elem` show x
         where (avg, m) = divMod (a007953 x) (a055642 x)
-- Reinhard Zumkeller, Jun 18 2013

Crossrefs

Cf. A007953, A055642, A004426, A004427; A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539.

Cf. A052018. - Reinhard Zumkeller, Aug 15 2010

Sequence in context: A109872 A030285 A283870 * A048321 A071267 A295010

Adjacent sequences: A175685 A175686 A175687 * A175689 A175690 A175691

Keyword

base,nonn

Author

Claudio Meller, Aug 09 2010

Extensions

Edited by Reinhard Zumkeller, Aug 13 2010

Status

approved