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

Author

Amarnath Murthy, May 03 2001

Keywords

• nonn
• easy
• base

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

Examples

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

Links

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

Crossrefs

Cf. A007953, A055642.

Cf. A004426, A004427.

Cf. A175688, A180157, A180160.

Programs

Haskell

a061383 n = a061383_list !! (n-1)
a061383_list = filter (\x -> mod (a007953 x) (a055642 x) == 0) [0..]
-- Reinhard Zumkeller, Jun 18 2013

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

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 *)

PARI

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

Python

def ok(n): return n == 0 or sum(d:=list(map(int, str(n))))%len(d) == 0
print([k for k in range(130) if ok(k)]) # Michael S. Branicky, Apr 23 2025