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A328095
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Revenant numbers: numbers k such that k multiplied by the product of all its digits contains k as a substring.
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12
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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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
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REFERENCES
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Eric Angelini, Posting to Sequence Fans Mailing List, Oct 19 2019
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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Select[Range[0, 10000], SequenceCount[IntegerDigits[#*(Times@@IntegerDigits[ #])], IntegerDigits[#]]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 19 2019 *)
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PROG
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(Python)
from functools import reduce
from operator import mul
sn = str(n)
if sn in str(n*reduce(mul, (int(d) for d in sn))):
(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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