# [seqfan] exotic numbers: A064818

Douglas McNeil mcneil at hku.hk
Tue Sep 7 07:10:06 CEST 2010

```Searching for keyword:nice+keyword:more revealed this:

--
A064818  	 	 Exotic numbers: write n in base 10 as d_1 d_2 ... d_k;
sequence gives numbers n which can be obtained by using the digits d_1
... d_k exactly once, at most one each of the symbols +, -, x,
"divided by", sqrt, factorial, ^, together with any number of
parentheses.

1, 2, 24, 25
--

Several other terms of the sequence are listed in the comments.  I
believe I can confirm the first seven terms of the sequence are

[1,2,24,25,36,64, 71]

Probably the sequence up to 1000 is:

[1, 2, 24, 25, 36, 64, 71, 120, 121, 125, 126, 127, 128, 153, 184,
216, 289, 324, 337, 343, 347, 354, 355, 360, 384, 456, 464, 624, 625,
648, 660, 688, 693, 720, 729, 736]

with about 10% chance of rain.  The algorithm should find every
solution, and it correctly found all constructions noted in the
comments except for 144 (which uses two + and ! symbols and so is
inadmissible.)  Can anyone confirm or correct?

Doug

--
Department of Earth Sciences
University of Hong Kong

```