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

1,2

Comments

First term greater than 9 without digit 0 is 119.

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

Links

Table of n, a(n) for n=1..54.

Example

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.

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 *)

Crossrefs

Cf. A007953, A007954, A052018, A227510.

Sequence in context: A236402 A052018 A352461 * A202272 A180480 A080459

Adjacent sequences: A302765 A302766 A302767 * A302769 A302770 A302771

Keyword

nonn,base,easy

Author

Paolo P. Lava, Apr 13 2018

Status

approved