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

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 109, 119, 200, 300, 400, 500, 600, 700, 800, 900, 910, 911, 1000, 1009, 1018, 1027, 1036, 1045, 1054, 1063, 1072, 1081, 1090, 1108, 1109, 1118, 1181, 1190, 1209, 1236, 1290, 1309, 1390, 1409, 1490

Offset: 1

Author

Paolo P. Lava, Apr 13 2018

Keywords

• nonn
• base
• easy

Comments

First term greater than 9 without digit 0 is 119.

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

Examples

			911 => 9 + 1 + 1 = 11 and 9 * 1 * 1 = 9;
1309 => 1 + 3 + 0 + 9 = 13 and 1 * 3 * 0 * 9 = 0;
3499236 => 3 + 4 + 9 + 9 + 2 + 3 + 6 = 36 and 3 * 4 * 9 * 9 * 2 * 3 * 6 = 34992.
		

Crossrefs

Cf. A007953, A007954, A052018, A227510.

Programs

Maple

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]);

Mathematica

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