# [seqfan] Re: puzzled by A082945, definition of rev n

Richard Mathar mathar at strw.leidenuniv.nl
Fri Apr 17 20:33:37 CEST 2009

```mh> From maximilian.hasler at gmail.com Fri Apr 17 19:25:10 2009
mh> Subject: Re: [seqfan] puzzled by A082945, definition of rev n
mh> To: Richard Mathar <mathar at strw.leidenuniv.nl>
mh> Cc: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
mh>
mh> A082945 Numbers starting with n such that n/(rev n) is the center
mh> digit, where (rev n) is the reverse of n.
mh> 111, 212, 221, 313, 331, 414, 422, 441, 515, 551, 616, 623, 632, 661,
mh> 717, 771, 818, 824, 842, 881, 919, 933, 991
mh>
mh> I think here it (rev n) means the last digit when n is the first digit
mh> and probably  the reversal of the last k digits when n are the first k digits.
mh> (A priori any positive k <= number of digits of a(m)  seems allowed.)
mh> ...

This seems to be closer to the truth but is insufficient.

We could for example consider 250, take 25 as n (with k=2), read  the last
k=2 digits and revert, that is rev(50) = 05 = 5, and 25/5 =5 is the
middle digit. This puts 250 into the sequence.
Again with k=2, we could place 360 (n=36, rev(n) = 06=6, n/rev(n)=6) into the
sequence.
With k=2, we also would have 751 (n=75, rev(n)=rev(51)=15, 75/15=5, the
middle digit) in the sequence.
Again with k=2, we could place 961 (n=96, rev(n)=rev(61)=16, 96/16=6) into the
sequence.
To explain why these examples 250, 360, 751, 961 etc are not in the sequence,
some sort of non-overlapping condition must be added to get what's currently
seen in http://www.research.att.com/~njas/sequence/A082945 .

mh> Maximilian
mh> PS: IMHO these sequences are not extremely interesting...

I definitely agree.

```