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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. 7
 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)
 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 Chai Wah Wu, Table of n, a(n) for n = 1..10000 Eric Angelini, Revenant Numbers, Cinquante Signes, Oct 19 2019. FORMULA A328560 union A328561. 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 Adjacent sequences:  A328092 A328093 A328094 * A328096 A328097 A328098 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Oct 19 2019 STATUS approved

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Last modified November 19 03:27 EST 2019. Contains 329310 sequences. (Running on oeis4.)