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

Author

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

Keywords

• easy
• nonn
• base

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A070565.

Programs

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

Extensions

Corrected by Robert Israel, Jul 22 2025