A061383 Arithmetic mean of digits is an integer.

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, 42, 44, 46, 48, 51, 53, 55, 57, 59, 60, 62, 64, 66, 68, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 91, 93, 95, 97, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129

Offset

0,3

Comments

A004426(a(n)) = A004427(a(n)). - Reinhard Zumkeller, May 27 2010

A175688 is a subsequence; complement of A180157; A180160(a(n))=0. - Reinhard Zumkeller, Aug 15 2010

It seems "obvious" that n log n << a(n) < n log n; is this true? - Charles R Greathouse IV, Feb 06 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Example

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

Mathematica

Select[Range[0, 129], IntegerQ[Total[x=IntegerDigits[#]]/Length[x]] &] (* Jayanta Basu, May 17 2013 *)
Select[Range[0, 200], IntegerQ[Mean[IntegerDigits[#]]]&] (* Harvey P. Dale, Dec 31 2022 *)

Prog

(Magma) [0] cat [n: n in [1..130] | IsZero(&+Intseq(n) mod #Intseq(n))];  // Bruno Berselli, Jun 30 2011
(Magma) [0] cat [n: n in [1..130] | IsIntegral(&+Intseq(n)/#Intseq(n))];   // Bruno Berselli, Feb 09 2016
(PARI) is(n)=my(v=digits(n)); sum(i=1, #v, v[i])%#v==0 \\ Charles R Greathouse IV, Feb 06 2013
(Haskell)
a061383 n = a061383_list !! (n-1)
a061383_list = filter (\x -> mod (a007953 x) (a055642 x) == 0) [0..]
-- Reinhard Zumkeller, Jun 18 2013

Crossrefs

Cf. A007953, A055642.

Cf. A004426, A004427.

Cf. A175688, A180157, A180160.

Sequence in context: A191839 A032959 A275945 * A059708 A306520 A247945

Adjacent sequences: A061380 A061381 A061382 * A061384 A061385 A061386

Keyword

nonn,easy,base

Author

Amarnath Murthy, May 03 2001

Status

approved