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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.

%I A134942 #17 Jul 23 2025 00:54:03
%S A134942 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,
%T A134942 56,57,61,62,63,65,67,68,69,71,72,75,76,77,78,79,81,83,84,85,86,87,88,
%U A134942 89,91,92,93,94,95,96,97,98,99,121,123,127,129,132,133,136,139,141,143
%N 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.
%C A134942 Obviously no number containing a zero digit is in the sequence.
%H A134942 Robert Israel, <a href="/A134942/b134942.txt">Table of n, a(n) for n = 1..10000</a>
%e A134942 For 0 <= p <= 9, p - P(p) = 0, hence 0 is not in the sequence.
%e A134942 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.
%p A134942 f:= n -> n - convert(convert(n,base,10),`*`):
%p A134942 R:= {}:
%p A134942 S:= {0}:
%p A134942 for d from 1 to 3 do
%p A134942   S:= map(proc(t) local i; seq(10*t+i,i=1..9) end proc, S);
%p A134942   V:= S minus map(f, S);
%p A134942   R:= R union V;
%p A134942 od:
%p A134942 sort(convert(R,list)); # _Robert Israel_, Jul 22 2025
%Y A134942 Cf. A070565.
%K A134942 easy,nonn,base
%O A134942 1,2
%A A134942 Philippe Lallouet (philip.lallouet(AT)orange.fr), Feb 01 2008
%E A134942 Corrected by _Robert Israel_, Jul 22 2025