A248210 -id:A248210 - cp's OEIS frontend

A248717 Zeroless numbers k such that k - (sum of digits of k) and k - (product of digits of k) contain the same distinct digits as k.

12331, 13231, 13651, 21331, 23131, 23552, 25545, 26553, 31231, 31651, 32131, 32552, 34355, 34531, 34554, 35354, 35453, 35631, 36156, 36231, 43531, 45353, 46431, 53631, 54353, 54885, 55245, 55296, 59652, 61599, 63231, 64431, 87973, 95274, 122553, 125918, 126531, 126535, 126553

Offset: 1

Derek Orr, Oct 12 2014

Intersection of A248209 and A248210. If a number k contains a zero, it automatically holds the property that k - (product of digits of k) contains the same distinct digits as k. - Tanya Khovanova, Jul 18 2021

"The same distinct digits" in the title means the same set of digits ignoring multiplicities. - Tanya Khovanova, Jul 18 2021

Cf. A248209, A248210, A007954, A007953.

Select[Range@100000,(d=IntegerDigits@#;FreeQ[d,0]&&Union@IntegerDigits[#-Times@@d]==Union@d==Union@IntegerDigits[#-Total@d])&] (* Giorgos Kalogeropoulos, Jul 20 2021 *)

for(n=0, 10^6, d=digits(n); p=prod(i=1, #d, d[i]); vp=vecsort(digits(p-n), , 8); vs=vecsort(digits(sumdigits(n)-n), , 8); if(vs==vp&&vp==vecsort(d, , 8)&&vs==vecsort(d, , 8)&&p, print1(n, ", ")))

from math import prod
def ok(n):
    s = str(n); d = list(map(int, s))
    if '0' in s: return False
    return set(s) == set(str(n-sum(d))) and set(s) == set(str(n-prod(d)))
print(list(filter(ok, range(127000)))) # Michael S. Branicky, Jul 18 2021

cp's OEIS Frontend

A248717 Zeroless numbers k such that k - (sum of digits of k) and k - (product of digits of k) contain the same distinct digits as k.

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