[seqfan] Revenant numbers

[Éric Angelini]

Hello SeqFans (cross-posted on Math-Fun),
Take an integer abc...z and multiply it by all its digits: if the string abc...z appears in the result, we have a "revenant number".

Look at 87 for instance: 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 9375 as 9375 * 9 * 3 * 7 * 5 = 8859375.

If we start a sequence R of revenants we'll get (not in the OEIS):

R = 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,...

R is infinite, of course, as all repunits (like 11, 111, 1111, 1111,...) will be in R.

Will you find the next revenant > 62227496 whose "image" doesn't show any zero?

More details, DiCaprio and a graph here:
http://cinquantesignes.blogspot.com/2019/10/revenant-numbers.html

Best,
É.