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

Author

Eric Angelini, May 22 2007

Keywords

• base
• easy
• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A038365 (complement).

Programs

Haskell

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

Maple

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

Mathematica

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

Extensions

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