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A344375 Numbers n that can be written as the concatenation ab such that n mod (a*b) = a+b.

%I A344375 #15 May 16 2021 21:27:44
%S A344375 23,29,33,39,43,49,53,59,63,69,73,79,83,89,93,99,103,109,113,119,123,
%T A344375 129,133,139,143,149,153,159,163,169,173,179,183,189,193,199,203,209,
%U A344375 211,213,219,223,229,233,239,243,249,253,259,263,269,273,279,283,289,293,299,303,309,311,313,319,323
%N A344375 Numbers n that can be written as the concatenation ab such that n mod (a*b) = a+b.
%C A344375 Leading zeros are not allowed in b.
%C A344375 Includes all n >= 23 with n == 3 or 9 (mod 10), and all n >= 211 with n == 11 (mod 100).
%C A344375 Are there terms not of these forms?
%C A344375 Includes forms n == 142857 (mod 1000000) for n >= 2142857. - _Michael S. Branicky_, May 16 2021
%H A344375 Robert Israel, <a href="/A344375/b344375.txt">Table of n, a(n) for n = 1..10000</a>
%e A344375 a(25) = 143 is a term because 143 mod (14*3) = 17 = 14+3.
%p A344375 filter:= proc(n) local k,a,b;
%p A344375   for k from 1 to ilog10(n) do
%p A344375     a:= n mod 10^k;
%p A344375     b:= (n-a)/10^k;
%p A344375     if a < 10^(k-1) then next fi;
%p A344375     if n mod (a*b) = a+b then return true fi
%p A344375   od;
%p A344375   false
%p A344375 end proc:
%p A344375 select(filter, [$10..1000]);
%o A344375 (Python)
%o A344375 def ok(n):
%o A344375   s = str(n)
%o A344375   for i in range(1, len(s)):
%o A344375     if s[i] == '0': continue
%o A344375     a, b = int(s[:i]), int(s[i:])
%o A344375     if n%(a*b) == a+b: return True
%o A344375   return False
%o A344375 print(list(filter(ok, range(1, 324)))) # _Michael S. Branicky_, May 16 2021
%Y A344375 Cf. A268044.
%K A344375 nonn,base
%O A344375 1,1
%A A344375 _J. M. Bergot_ and _Robert Israel_, May 16 2021