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A248210 Zeroless numbers k (numbers in A052382) such that k - DigitProduct(k) contains the same distinct digits as k. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

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

MATHEMATICA

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

PROG

(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

CROSSREFS

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

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

Sequence in context: A202888 A217181 A155140 * A142284 A245583 A252409

Adjacent sequences: A248207 A248208 A248209 * A248211 A248212 A248213

KEYWORD

nonn,easy,base

AUTHOR

Derek Orr, Oct 03 2014

STATUS

approved

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Last modified January 28 01:36 EST 2023. Contains 359849 sequences. (Running on oeis4.)