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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
MATHEMATICA
Select[Range@100000, (d=IntegerDigits@#; FreeQ[d, 0]&&Union@IntegerDigits[#-Times@@d]==Union@d==Union@IntegerDigits[#-Total@d])&] (* Giorgos Kalogeropoulos, Jul 20 2021 *)
PROG
(PARI) 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, ", ")))
(Python)
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
CROSSREFS
Sequence in context: A277947 A321492 A237782 * A184472 A350153 A251949
KEYWORD
nonn,base
AUTHOR
Derek Orr, Oct 12 2014
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)