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

293, 362, 436, 545, 554, 631, 653, 749, 763, 891, 958, 965, 1293, 1362, 1436, 1545, 1554, 1631, 1653, 1749, 1763, 1891, 1958, 1965, 2193, 2331, 2491, 2536, 2556, 2565, 2693, 2917, 2954, 2963, 3162, 3231, 3325, 3382, 3529, 3534, 3635, 3651, 4291, 4515, 4533, 4551, 4634, 4935, 4952, 4971

Offset: 1

Author

Derek Orr, Oct 03 2014

Keywords

• nonn
• easy
• base

Comments

Numbers that contain zeros trivially have this property. - Tanya Khovanova, Jul 19 2021

Examples

			631 - 6*3*1 = 613 contains the same digits as 631. So 631 is a term of this sequence.
		

Crossrefs

Cf. A052382 (zeroless numbers), A007954 (digit product).

Cf. A247888 (similar, with n + digit product).

Programs

Mathematica

Select[Range@5000,(d=IntegerDigits@#;FreeQ[d,0]&&Union@IntegerDigits[#-Times@@d]==Union@d)&] (* Giorgos Kalogeropoulos, Jul 20 2021 *)

PARI

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, ", ")))

Python

from math import prod
def ok(n):
    s = str(n)
    return '0' not in s and set(str(n-prod(int(d) for d in s))) == set(s)
print(list(filter(ok, range(5000)))) # Michael S. Branicky, Jul 18 2021