A241142 Numbers n such that n and 6n share at least one digit.

2, 4, 6, 8, 10, 12, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 34, 36, 38, 39, 40, 41, 42, 44, 46, 48, 49, 50, 52, 53, 54, 56, 58, 59, 60, 61, 62, 63, 64, 66, 68, 70, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88, 90, 92, 94, 95, 96, 98, 99, 100

Offset: 1

Author

Robert G. Wilson v, Apr 16 2014

Keywords

• base
• easy
• nonn

Comments

All numbers n which are congruent to 0 (mod 6) have this characteristic.

All even n have this characteristic, because n == 6n mod 10. Robert Israel, Apr 17 2014

Examples

			12 is in the sequence since 12 and 6*12 = 72 and together they share the digit 2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A129845, A129846, A129848, A241141, A241143, A241144, A241145, A241146.

Programs

Maple

  N:= 10000;  # to get all entries up to N
filter:= proc(n) local L, L6;
   L:= convert(convert(n,base,10),set);
   L6:= convert(convert(6*n,base,10),set);
   L intersect L6 <> {};
end;
select(filter, [$1..N]); # Robert Israel, Apr 17 2014

Mathematica

fQ[n_] := Intersection[ IntegerDigits[ n], IntegerDigits[6 n]] != {}; Select[ Range[ 100], fQ]

PARI

isok(n) = #setintersect(Set(digits(n)), Set(digits(6*n))); \\ Michel Marcus, Apr 17 2014