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A248210 Zeroless numbers k (numbers in A052382) such that k - DigitProduct(k) contains the same distinct digits as k.

%I A248210 #39 May 06 2022 13:13:51
%S A248210 293,362,436,545,554,631,653,749,763,891,958,965,1293,1362,1436,1545,
%T A248210 1554,1631,1653,1749,1763,1891,1958,1965,2193,2331,2491,2536,2556,
%U A248210 2565,2693,2917,2954,2963,3162,3231,3325,3382,3529,3534,3635,3651,4291,4515,4533,4551,4634,4935,4952,4971
%N A248210 Zeroless numbers k (numbers in A052382) such that k - DigitProduct(k) contains the same distinct digits as k.
%C A248210 Numbers that contain zeros trivially have this property. - _Tanya Khovanova_, Jul 19 2021
%e A248210 631 - 6*3*1 = 613 contains the same digits as 631. So 631 is a term of this sequence.
%t A248210 Select[Range@5000,(d=IntegerDigits@#;FreeQ[d,0]&&Union@IntegerDigits[#-Times@@d]==Union@d)&] (* _Giorgos Kalogeropoulos_, Jul 20 2021 *)
%o A248210 (PARI)
%o A248210 for(n=1, 10^4, d=digits(n); p=prod(i=1, #d, d[i]); if(p && vecsort(digits(n), , 8)==vecsort(digits(n-p), , 8), print1(n, ", ")))
%o A248210 (Python)
%o A248210 from math import prod
%o A248210 def ok(n):
%o A248210     s = str(n)
%o A248210     return '0' not in s and set(str(n-prod(int(d) for d in s))) == set(s)
%o A248210 print(list(filter(ok, range(5000)))) # _Michael S. Branicky_, Jul 18 2021
%Y A248210 Cf. A052382 (zeroless numbers), A007954 (digit product).
%Y A248210 Cf. A247888 (similar, with n + digit product).
%K A248210 nonn,easy,base
%O A248210 1,1
%A A248210 _Derek Orr_, Oct 03 2014