cp's OEIS Frontend

A302768 Numbers k whose sum and product of digits are substrings of k.

%I A302768 #21 Apr 28 2018 17:59:30
%S A302768 1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100,109,119,200,300,400,
%T A302768 500,600,700,800,900,910,911,1000,1009,1018,1027,1036,1045,1054,1063,
%U A302768 1072,1081,1090,1108,1109,1118,1181,1190,1209,1236,1290,1309,1390,1409,1490
%N A302768 Numbers k whose sum and product of digits are substrings of k.
%C A302768 First term greater than 9 without digit 0 is 119.
%C A302768 First term greater than 9 without digits 0 and 1 is 3499236.
%e A302768 911 => 9 + 1 + 1 = 11 and 9 * 1 * 1 = 9;
%e A302768 1309 => 1 + 3 + 0 + 9 = 13 and 1 * 3 * 0 * 9 = 0;
%e A302768 3499236 => 3 + 4 + 9 + 9 + 2 + 3 + 6 = 36 and 3 * 4 * 9 * 9 * 2 * 3 * 6 = 34992.
%p A302768 select(n->searchtext(convert(convert(convert(n, base, 10), `+`),string),x.n)*searchtext(convert(convert(convert(n, base, 10), `*`),string),x.n)>0,[$1..1500]);
%t A302768 Select[Range@ 1500, With[{d = IntegerDigits[#]}, AllTrue[IntegerDigits@ {Total@ d, Times @@ d}, SequenceCount[d, #] > 0 &]] &] (* _Michael De Vlieger_, Apr 21 2018 *)
%Y A302768 Cf. A007953, A007954, A052018, A227510.
%K A302768 nonn,base,easy
%O A302768 1,2
%A A302768 _Paolo P. Lava_, Apr 13 2018