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A302768
Numbers k whose sum and product of digits are substrings of k.
0
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.
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
KEYWORD
nonn,base,easy
AUTHOR
Paolo P. Lava, Apr 13 2018
STATUS
approved