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A328095
Revenant numbers: numbers k such that k multiplied by the product of all its digits contains k as a substring.
12
0, 1, 5, 6, 11, 25, 52, 77, 87, 111, 125, 152, 215, 251, 375, 376, 455, 512, 521, 545, 554, 736, 792, 1111, 1125, 1152, 1215, 1251, 1455, 1512, 1521, 1545, 1554, 2115, 2151, 2174, 2255, 2511, 2525, 2552, 4155, 4515, 4551, 5112, 5121, 5145, 5154, 5211, 5225, 5252, 5415, 5451, 5514, 5522, 5541, 5558, 5585, 5855, 8555, 8772, 9375
OFFSET
1,3
COMMENTS
Sequence is infinite since 11...1 is always a member.
Numbers whose product of digits is a power of ten (and thus necessarily must only have 1,2,4,5,8 as digits) is a subsequence. - Chai Wah Wu, Oct 19 2019
REFERENCES
Eric Angelini, Posting to Sequence Fans Mailing List, Oct 19 2019
LINKS
Eric Angelini, Revenant Numbers, Cinquante Signes, Oct 19 2019.
FORMULA
EXAMPLE
87 * 8 * 7 = 4872. As the string 87 is visible in the result, 87 is a revenant.
So is 792 because 792 * 7 * 9 * 2 = 99792.
And so is 9375 as 9375 * 9 * 3 * 7 * 5 = 8859375.
MAPLE
a:= proc(n) option remember; local k; if n=1 then 0 else
for k from 1+a(n-1) while searchtext(cat(k), cat(k*
mul(i, i=convert(k, base, 10))))=0 do od: k fi
end:
seq(a(n), n=1..75); # Alois P. Heinz, Oct 19 2019
MATHEMATICA
Select[Range[0, 10000], SequenceCount[IntegerDigits[#*(Times@@IntegerDigits[ #])], IntegerDigits[#]]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 19 2019 *)
PROG
(Python)
from functools import reduce
from operator import mul
n, A328095_list = 0, []
while len(A328095_list) < 10000:
sn = str(n)
if sn in str(n*reduce(mul, (int(d) for d in sn))):
A328095_list.append(n)
n += 1 # Chai Wah Wu, Oct 19 2019
(PARI) is_A328095(n)={my(d, m); if(d=vecprod(digits(n))*n, m=10^logint(n, 10)*10; until(n>d\=10, d%m==n && return(1)), !n)} \\ M. F. Hasler, Oct 20 2019
CROSSREFS
Subsequences are: A328544, A328560, A328561.
Sequence in context: A020685 A275492 A046828 * A046830 A042493 A042217
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Oct 19 2019
STATUS
approved