A267795 Integers n such that n, 2n, 3n ... 10n contain almost equally many copies of each base 10 digit.

1, 9, 109, 909, 10909, 90909, 1090909, 9090909, 13431958, 25834963, 32973507, 38296415, 45096237, 51546969, 94845303, 96237045, 109090909, 113431958, 126084879, 132868745, 132875488, 133595248, 134319558, 134755956, 134758658, 137584878, 143865844, 153584878

Offset: 1

Author

Jack W Grahl, Jan 20 2016

Keywords

• nonn
• easy
• base

Comments

Here 'almost equally many' means that the most common digit appears only once more than the least common.

Examples

			The first 10 multiples of 109 are 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090. Every digit appears 3 times except for '1' which appears 4 times. It is clear that all numbers of the form 10909..0909 and 90909..0909 appear in the list, and it seems likely that these are the only members.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A038365.

Programs

Python

def f(n):
  """ This returns True iff n is in the sequence """
  l = [ n * i for i in range(1, 11) ]
  s = "".join(str(i) for i in l)
  c = [ s.count(str(j)) for j in range(10) ]
  return min(c) >= max(c) - 1
for n in range(1, 10000000):
  if f(n):
    print(n, end=', ')

Extensions

a(7)-a(28) from Lars Blomberg, Aug 11 2016