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URL: https://oeis.org/A344375

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A344375
Numbers n that can be written as the concatenation ab such that n mod (a*b) = a+b.
1
23, 29, 33, 39, 43, 49, 53, 59, 63, 69, 73, 79, 83, 89, 93, 99, 103, 109, 113, 119, 123, 129, 133, 139, 143, 149, 153, 159, 163, 169, 173, 179, 183, 189, 193, 199, 203, 209, 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
OFFSET
1,1
COMMENTS
Leading zeros are not allowed in b.
Includes all n >= 23 with n == 3 or 9 (mod 10), and all n >= 211 with n == 11 (mod 100).
Are there terms not of these forms?
Includes forms n == 142857 (mod 1000000) for n >= 2142857. - Michael S. Branicky, May 16 2021
LINKS
EXAMPLE
a(25) = 143 is a term because 143 mod (14*3) = 17 = 14+3.
MAPLE
filter:= proc(n) local k, a, b;
for k from 1 to ilog10(n) do
a:= n mod 10^k;
b:= (n-a)/10^k;
if a < 10^(k-1) then next fi;
if n mod (a*b) = a+b then return true fi
od;
false
end proc:
select(filter, [$10..1000]);
PROG
(Python)
def ok(n):
s = str(n)
for i in range(1, len(s)):
if s[i] == '0': continue
a, b = int(s[:i]), int(s[i:])
if n%(a*b) == a+b: return True
return False
print(list(filter(ok, range(1, 324)))) # Michael S. Branicky, May 16 2021
CROSSREFS
Cf. A268044.
Sequence in context: A244077 A277206 A214754 * A153631 A382239 A382237
KEYWORD
nonn,base
AUTHOR
J. M. Bergot and Robert Israel, May 16 2021
STATUS
approved