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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

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<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

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

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Last modified October 18 18:47 EDT 2021. Contains 348068 sequences. (Running on oeis4.)