# [seqfan] Re: A177045: ordering of expressions built from numbers 2 and exponentiations

franktaw at netscape.net franktaw at netscape.net
Thu May 6 22:31:37 CEST 2010

```One should be able to get two more "generations" by taking the log base
2 twice before evaluating. The first log gives you a product, and the
second produces a sum of products.  For example,
((2^(2^2))^2)^(2^(2^2)) => 2^2 * 2 * 2^(2^2) => 2 + 1 + 2^2 = 7.

(I don't know whether Douglas is already doing this.)

-----Original Message-----
From: Douglas McNeil <mcneil at hku.hk>

I believe I can confirm the submitted terms.  The early ones are
straightforward (though doubtless not so straightforward that they're
beyond Murphy's reach) as we know that the terms which are easy to
deal with because they're small precede the terms which are harder to
compare.

VR:
[1, 2, 3, 4, 7, 8, 9, 5, 6, 17, 18, 21]

sage: mi[11][:100]
[1, 2, 3, 4, 7, 8, 9, 5, 6, 17, 18, 21, 22, 23, 15, 16, 19, 20, 49,
50, 51, 59, 60, 63, 64, 65, 43, 44, 45, 46, 47, 48, 57, 58, 61, 62,
149, 150, 153, 154, 155, 181, 182, 183, 191, 192, 195, 196, 197, 136,
137, 138, 139, 140, 141, 147, 148, 151, 152, 175, 176, 177, 178, 179,
180, 189, 190, 193, 194, 478, 479, 480, 488, 489, 492, 493, 494, 578,
579, 582, 583, 584, 610, 611, 612, 620, 621, 624, 625, 626, 12, 13,
14, 132, 133, 134, 135, 439, 440, 441]

Doug

```