[seqfan] Richard Guy's request for several new sequences (amended)

N. J. A. Sloane njas at research.att.com
Sun Jan 15 21:39:50 CET 2012

I forgot one important thing. This message replaces the one
I sent a few minutes ago.

Dear SeqFans (and Richard)

Richard Guy has been investigating recurrences
satisfied by A023110 and related sequences - there
are some surprising connections with continued
factions. He has a very interesting preprint 
called "Neg and Reg", which he would probably
be willing to send to anyone who was interested.

A023110 is the central sequence: this lists squares
which remain square when their last decimal digit is deleted.
Their square roots are A204132. The truncated squares
are A202303, and their square roots are (essentially) A031150.

So for base 10 we have A023110, A204132, A202303, A031150.
We need analogs of these 4 sequences for bases 2 through 9.

For each base 2 through 9 we need the analogues
of these four sequences, written both in base 10
and in the defining base. So there will be eight
sequences for each base.

Some will be in the OEIS already.
Please help fill in the gaps.


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