A134942 Numbers m such that there exists no number k with k-P(k) = m, where P(k) is the product of digits of k written in base 10.

1, 2, 3, 4, 5, 6, 7, 8, 9, 21, 23, 27, 29, 32, 33, 36, 39, 41, 43, 44, 47, 48, 49, 51, 53, 54, 56, 57, 61, 62, 63, 65, 67, 68, 69, 71, 72, 75, 76, 77, 78, 79, 81, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 121, 123, 127, 129, 132, 133, 136, 139, 141, 143

Offset

1,2

Comments

Obviously no number containing a zero digit is in the sequence.

Links

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

Example

For 0 <= p <= 9, p - P(p) = 0, hence 0 is not in the sequence.
It's easy to see that if p has 2 digits or more the difference p - P(p) has at least 2 digits, hence 1 to 9 are in the sequence.

Maple

f:= n -> n - convert(convert(n, base, 10), `*`):
R:= {}:
S:= {0}:
for d from 1 to 3 do
  S:= map(proc(t) local i; seq(10*t+i, i=1..9) end proc, S);
  V:= S minus map(f, S);
  R:= R union V;
od:
sort(convert(R, list)); # Robert Israel, Jul 22 2025

Crossrefs

Cf. A070565.

Sequence in context: A098951 A097962 A247813 * A122639 A344748 A342810

Adjacent sequences: A134939 A134940 A134941 * A134943 A134944 A134945

Keyword

easy,nonn,base

Author

Philippe Lallouet (philip.lallouet(AT)orange.fr), Feb 01 2008

Extensions

Corrected by Robert Israel, Jul 22 2025

Status

approved