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A307751
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Numbers k such that the number m multiplied by the product of all its digits contains k as a substring, where m = k multiplied by the product of all its digits.
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0
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0, 1, 5, 6, 7, 11, 19, 79, 84, 111, 123, 176, 232, 396, 1111, 11111, 111111, 331788, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, 1111111111111, 11111111111111, 111111111111111
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OFFSET
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1,3
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COMMENTS
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Inspired by A328095. Like A328095 this sequence contains all the repunits. These numbers could be called 'Two-step Revenant numbers'. It is unknown if 331788 is the last non-repunit.
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LINKS
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EXAMPLE
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79 is in the sequence as m = 79*7*9 = 4977, and 4977*4*9*7*7 = 8779428, and '8779428' contains '79' as a substring.
331788 is in the sequence as m = 331788*3*3*1*7*8*8 = 1337769216, and 1337769216*1*3*3*7*7*6*9*2*1*6 = 382291633317888, and '382291633317888' contains '331788' as a substring.
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MATHEMATICA
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f[n_] := n * Times @@ IntegerDigits[n]; aQ[n_] := SequenceCount[IntegerDigits[ f[f[n]] ], IntegerDigits[n]] > 0; Select[Range[0, 10^6], aQ] (* Amiram Eldar, Nov 10 2019 *)
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PROG
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(Magma) a:=[0]; f:=func<n|n*(&*Intseq(n))>; for k in [1..1200000] do t:=IntegerToString(f(f(k))); s:=IntegerToString(k); if s in t then Append(~a, k); end if; end for; a; // Marius A. Burtea, Nov 10 2019
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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