A344375 Numbers n that can be written as the concatenation ab such that n mod (a*b) = a+b.
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
Examples
a(25) = 143 is a term because 143 mod (14*3) = 17 = 14+3.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A268044.
Programs
-
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]); -
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
Comments