

A175688


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


5



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
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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 !! (n1)
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



