

A307751


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.


0



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

1,3


COMMENTS

Inspired by A328095. Like A328095 this sequence contains all the repunits. These numbers could be called 'Twostep Revenant numbers'. It is unknown if 331788 is the last nonrepunit.


LINKS

Table of n, a(n) for n=1..27.
Eric Angelini, Revenant Numbers, Cinquante Signes, Oct 19 2019.


EXAMPLE

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.


MATHEMATICA

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 *)


PROG

(MAGMA) a:=[0]; f:=func<nn*(&*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


CROSSREFS

Cf. A328095, A326806, A328544.
Sequence in context: A300957 A139205 A288859 * A039589 A028318 A154952
Adjacent sequences: A307748 A307749 A307750 * A307752 A307753 A307754


KEYWORD

nonn,base,more


AUTHOR

Scott R. Shannon, Nov 10 2019


EXTENSIONS

a(24)a(27) from Giovanni Resta, Nov 15 2019


STATUS

approved



