# [seqfan] Re: seqs whose |differences| are 1,2,3,4,...

franktaw at netscape.net franktaw at netscape.net
Thu Mar 11 05:37:54 CET 2010

```Neil,

Did you miss my note?  There is no lexicographically least permutation
with the specified difference property.  There are many permutations
with the property, but the greatest lower bound of these permutations
is the sequence Raff describes, and this is one-to-one but not onto.

There may be a sequence with the property such that the inverse
permutation is lexicographically least.  The algorithm I described is
"trying" to find this, but may not actually do so.

P.s. The sequence from Ron cannot be continued.  The next term must be
158; after that would have to be 4 or 312, both of which have already
been seen.

-----Original Message-----
From: N. J. A. Sloane <njas at research.att.com>

Ron,   This looks very nice!

> At the moment, this reaches all integers up to top=57
1 2 4 7 3 8 14 21 13 22 12 23 11 24 10 25 9 26 44 63 43 64 42 65 41 66
40 67 39
68 38 69 37 70 36 71 35 72 34 73 33 74 32 75 31 76 30 77 29 78 28 79 27
80 134 1
89 133 190 132 191 131 192 130 193 129 194 128 195 127 196 266 337 409
336 410
335 259 182 260 181 101 20 102 19 103 18 104 17 105 16 106 15 107 200
294 389
293 390 292 391 291 392 494 597 701 596 490 383 275 166 56 167 55 168
54 169 53
170 52 171 51 172 50 173 49 174 48 175 47 176 46 177 45 178 312 447 311
448 310
449 309 450 308 451 307 452 306 453 305 156 6 157 5

I am in Florida on a very slow connection so have not read all the
messages.

Supose you could run your program - or Paul's - for L = 100, 1000,
10000, etc.,
then the initial terms would stabilize, we hope, and we will get
more and more of the sequence we are looking for, which is the
limiting sequence.

Can you say how many terms of the sequence in your email will
be in the final answer?

That is, as you increase L, are we getting more
and more of the final answer, and if so how
much do we have so far.  I'm not asking for proofs,
just what your sense is after looking at the data!

Neil

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```