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A061383 Arithmetic mean of digits is an integer. 29

%I

%S 0,1,2,3,4,5,6,7,8,9,11,13,15,17,19,20,22,24,26,28,31,33,35,37,39,40,

%T 42,44,46,48,51,53,55,57,59,60,62,64,66,68,71,73,75,77,79,80,82,84,86,

%U 88,91,93,95,97,99,102,105,108,111,114,117,120,123,126,129

%N Arithmetic mean of digits is an integer.

%C A004426(a(n)) = A004427(a(n)). [From _Reinhard Zumkeller_, May 27 2010]

%C A175688 is a subsequence; complement of A180157; A180160(a(n))=0. [From _Reinhard Zumkeller_, Aug 15 2010]

%C It seems 'obvious' that n log n << a(n) < n log n; is this true? - _Charles R Greathouse IV_, Feb 06 2013

%H R. Zumkeller, <a href="/A061383/b061383.txt">Table of n, a(n) for n = 0..10000</a>

%e 123 is a term as the arithmetic mean is (1+2+3)/3 = 2.

%t Select[Range[0,129],IntegerQ[Total[x=IntegerDigits[#]]/Length[x]] &] (* _Jayanta Basu_, May 17 2013 *)

%o (MAGMA) [0] cat [n: n in [1..130] | IsZero(&+Intseq(n) mod #Intseq(n))]; // _Bruno Berselli_, Jun 30 2011

%o (MAGMA) [0] cat [n: n in [1..130] | IsIntegral(&+Intseq(n)/#Intseq(n))]; // _Bruno Berselli_, Feb 09 2016

%o (PARI) is(n)=my(v=digits(n));sum(i=1,#v,v[i])%#v==0 \\ _Charles R Greathouse IV_, Feb 06 2013

%o (Haskell)

%o a061383 n = a061383_list !! (n-1)

%o a061383_list = filter (\x -> mod (a007953 x) (a055642 x) == 0) [0..]

%o -- _Reinhard Zumkeller_, Jun 18 2013

%Y Cf. A007953, A055642.

%K nonn,easy,base

%O 0,3

%A _Amarnath Murthy_, May 03 2001

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Last modified April 23 03:26 EDT 2019. Contains 322380 sequences. (Running on oeis4.)