A328095 -id:A328095 - cp's OEIS frontend

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, 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

Offset: 1

Scott R. Shannon, Nov 10 2019

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.

			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.

Eric Angelini, Revenant Numbers, Cinquante Signes, Oct 19 2019.
Eric Angelini, Revenant Numbers, Cinquante Signes, Oct 19 2019. [Cached copy, pdf file, with permission]

Cf. A328095, A326806, A328544.

a:=[0]; f:=func; 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

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 *)

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

cp's OEIS Frontend

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.

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