A108193 - OEIS

%I #8 Mar 08 2020 21:37:17

%S 1,2,3,4,5,6,7,8,9,10,19,20,30,40,50,60,70,80,90,91,100,109,118,119,

%T 127,128,129,136,137,146,155,157,159,163,164,166,168,172,173,175,181,

%U 182,186,190,191,192,195,199,200,208,217,218,219,228

%N Numbers n such that n shares at least one digit with both the sum of its digits and the product of its digits.

%C Has A050278 as subsequence.

%H Robert Israel, <a href="/A108193/b108193.txt">Table of n, a(n) for n = 1..10000</a>

%e 238 shares the digit 3 with the sum of its digits (13) and shares the digit 8 with the product of its digits (48).

%p filter:= proc(n) local L,S,Ss,Sp;

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

%p   S:= convert(L,set);

%p   Ss:= convert(convert(convert(L,`+`),base,10),set);

%p   if S intersect Ss = {} then return false fi;

%p   Sp:= convert(convert(convert(L,`*`),base,10),set);

%p   S intersect Sp <> {}

%p end proc:

%p select(filter, [$1..500]); # _Robert Israel_, Mar 06 2020

%t Select[Range[0, 250], Length[Intersection[IntegerDigits[ # ], IntegerDigits[ Plus @@ IntegerDigits[ # ]]]] > 0 && Length[Intersection[IntegerDigits[ # ], IntegerDigits[Times @@ IntegerDigits[ # ]]]] > 0 &]

%Y Cf. A050278.

%K base,easy,nonn

%O 1,2

%A _Eric Angelini_, Jun 15 2005

%E Edited and corrected by _Stefan Steinerberger_, Jun 30 2007