[seqfan] Question on Smith numbers.

L. Edson Jeffery lejeffery2 at gmail.com
Sat Nov 26 05:05:38 CET 2016


The sequence of Smith numbers is http://oeis.org/A006753. Using a variant
of the Mathematica code written by Robert G. Wilson v in A006753, I seem to
be able to generate a sequence of arbitrary length, beginning as

{0, 1, 2, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 21, ...},

which lists the integers k >= 0 for which 22 + 36*k is a Smith number.

Is this sequence infinite? If it is, then is there an upper bound on the
first differences (I think not)?

Finally, are there other nontrivial equivalence classes of Smith numbers?

Ed Jeffery

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