A241142 - OEIS

%I #13 Apr 17 2014 18:17:21

%S 2,4,6,8,10,12,14,16,17,18,19,20,21,22,23,24,25,26,27,28,30,31,32,34,

%T 36,38,39,40,41,42,44,46,48,49,50,52,53,54,56,58,59,60,61,62,63,64,66,

%U 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

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

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

%C All even n have this characteristic, because n == 6n mod 10. _Robert Israel_, Apr 17 2014

%H Robert Israel, <a href="/A241142/b241142.txt">Table of n, a(n) for n = 1..10000</a>

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

%p   N:= 10000;  # to get all entries up to N

%p filter:= proc(n) local L, L6;

%p    L:= convert(convert(n,base,10),set);

%p    L6:= convert(convert(6*n,base,10),set);

%p    L intersect L6 <> {};

%p end;

%p select(filter, [$1..N]); # _Robert Israel_, Apr 17 2014

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

%o (PARI) isok(n) = #setintersect(Set(digits(n)), Set(digits(6*n))); \\ _Michel Marcus_, Apr 17 2014

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

%K base,easy,nonn

%O 1,1

%A _Robert G. Wilson v_, Apr 16 2014