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A267795
Integers n such that n, 2n, 3n ... 10n contain almost equally many copies of each base 10 digit.
1
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
1,2
COMMENTS
Here 'almost equally many' means that the most common digit appears only once more than the least common.
LINKS
EXAMPLE
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.
PROG
(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=', ')
CROSSREFS
Cf. A038365.
Sequence in context: A157906 A166846 A058421 * A128876 A199030 A288692
KEYWORD
nonn,easy,base
AUTHOR
Jack W Grahl, Jan 20 2016
EXTENSIONS
a(7)-a(28) from Lars Blomberg, Aug 11 2016
STATUS
approved