login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers k whose sum and product of digits are substrings of k.
0

%I #21 Apr 28 2018 17:59:30

%S 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 500,600,700,800,900,910,911,1000,1009,1018,1027,1036,1045,1054,1063,

%U 1072,1081,1090,1108,1109,1118,1181,1190,1209,1236,1290,1309,1390,1409,1490

%N Numbers k whose sum and product of digits are substrings of k.

%C First term greater than 9 without digit 0 is 119.

%C First term greater than 9 without digits 0 and 1 is 3499236.

%e 911 => 9 + 1 + 1 = 11 and 9 * 1 * 1 = 9;

%e 1309 => 1 + 3 + 0 + 9 = 13 and 1 * 3 * 0 * 9 = 0;

%e 3499236 => 3 + 4 + 9 + 9 + 2 + 3 + 6 = 36 and 3 * 4 * 9 * 9 * 2 * 3 * 6 = 34992.

%p 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 Select[Range@ 1500, With[{d = IntegerDigits[#]}, AllTrue[IntegerDigits@ {Total@ d, Times @@ d}, SequenceCount[d, #] > 0 &]] &] (* _Michael De Vlieger_, Apr 21 2018 *)

%Y Cf. A007953, A007954, A052018, A227510.

%K nonn,base,easy

%O 1,2

%A _Paolo P. Lava_, Apr 13 2018