A038365 -id:A038365 - cp's OEIS frontend

A129845 Numbers n such that n and 2n share at least one digit.

10, 12, 20, 21, 24, 25, 26, 30, 37, 40, 42, 47, 49, 50, 51, 60, 61, 62, 63, 68, 70, 71, 74, 75, 80, 81, 84, 87, 89, 90, 91, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 132, 137

Offset: 1

Eric Angelini, May 22 2007

The smallest term sharing more than one digit with its double is 102. - Alonso del Arte, Apr 16 2014

			10 is in the sequence because 2 * 10 = 20, which has a 0 in common with 10.
12 is in the sequence because 2 * 12 = 24, which has a 2 in common with 12.
14 is not in the sequence because 2 * 14 = 28, which has no digits in common with 14.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A038365 (complement).

a129845 n = a129845_list !! (n-1)
a129845_list =
   filter (\x -> not $ null (show (2*x) `intersect` show x)) [1..]
-- Reinhard Zumkeller, Aug 16 2011

a:=proc(n) if nops(convert(convert(n,base,10),set) intersect convert(convert(2*n,base,10),set))>0 then n else fi end: seq(a(n),n=1..170); # Emeric Deutsch, May 27 2007
isA129845 := proc(n) local twon,digsn,digs2n,i ; twon := 2*n ; digsn := convert(n,base,10) ; digs2n := convert(twon,base,10) ; for i from 1 to nops(digsn) do if op(i,digsn) in digs2n then RETURN(true) ; fi ; od ; RETURN(false) ; end: for n from 1 to 200 do if isA129845(n) then printf("%d, ",n) ; fi ; od ; # R. J. Mathar, Jun 08 2007

Select[Range[300], Length[Intersection[IntegerDigits[#], IntegerDigits[2#]]] > 0 &] (* Stefan Steinerberger, May 24 2007 *)

More terms from R. J. Mathar, Stefan Steinerberger and Emeric Deutsch, May 24 2007

A192825 Numbers m containing in decimal representation at least one zero and having no common digit in m and 2*m.

Original entry on oeis.org

207, 208, 209, 307, 308, 309, 406, 409, 606, 607, 609, 706, 707, 708, 709, 807, 808, 906, 907, 909, 2057, 2058, 2059, 2067, 2069, 2072, 2073, 2077, 2078, 2079, 2082, 2083, 2088, 2092, 2093, 2207, 2208, 2209, 2307, 2308, 2309, 2707, 2708, 2709, 2807, 2808

Offset: 1

Reinhard Zumkeller, Aug 09 2011

Intersection of A011540 and A038365; A168046(a(n)) = 0.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

import Data.List (intersect)
a192825 n = a192825_list !! (n-1)
a192825_list = filter (\x ->
   '0' `elem` show x && null (show (2*x) `intersect` show x)) [1..]

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

Original entry on oeis.org

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

Jack W Grahl, Jan 20 2016

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

			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.

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

Cf. A038365.

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=', ')

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

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A129845 Numbers n such that n and 2n share at least one digit.

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A192825 Numbers m containing in decimal representation at least one zero and having no common digit in m and 2*m.

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Haskell

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

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