A108193 Numbers n such that n shares at least one digit with both the sum of its digits and the product of its digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 20, 30, 40, 50, 60, 70, 80, 90, 91, 100, 109, 118, 119, 127, 128, 129, 136, 137, 146, 155, 157, 159, 163, 164, 166, 168, 172, 173, 175, 181, 182, 186, 190, 191, 192, 195, 199, 200, 208, 217, 218, 219, 228

Offset

1,2

Comments

Has A050278 as subsequence.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

238 shares the digit 3 with the sum of its digits (13) and shares the digit 8 with the product of its digits (48).

Maple

filter:= proc(n) local L, S, Ss, Sp;
  L:= convert(n, base, 10);
  S:= convert(L, set);
  Ss:= convert(convert(convert(L, `+`), base, 10), set);
  if S intersect Ss = {} then return false fi;
  Sp:= convert(convert(convert(L, `*`), base, 10), set);
  S intersect Sp <> {}
end proc:
select(filter, [$1..500]); # Robert Israel, Mar 06 2020

Mathematica

Select[Range[0, 250], Length[Intersection[IntegerDigits[ # ], IntegerDigits[ Plus @@ IntegerDigits[ # ]]]] > 0 && Length[Intersection[IntegerDigits[ # ], IntegerDigits[Times @@ IntegerDigits[ # ]]]] > 0 &]

Crossrefs

Cf. A050278.

Sequence in context: A280657 A117241 A108191 * A089583 A264979 A319726

Adjacent sequences: A108190 A108191 A108192 * A108194 A108195 A108196

Keyword

base,easy,nonn

Author

Eric Angelini, Jun 15 2005

Extensions

Edited and corrected by Stefan Steinerberger, Jun 30 2007

Status

approved