keystrokes display comments
14.072013 STO A 14.072013
LN 2.64418793126 ~ pi^2/6 + 1
pi ENTER * 6 / 1 + - 1/X +/- 1340.23897721 nothing interesting after trying a
few functions and multiples
RCL A sqrt sqrt sqrt sqrt 1.1797018602 again, nothing interesting here
RCL A 3 1/x y^x 2.41426761738 ~ sqrt(2) + 1 -- this looks promising
2 sqrt - 1 - 1/x STO B 18499.6728333
3 * 55499.0184999 here we have
(sqrt(2) + 1 + 3/55499)^3 = 14.0720130004
but the 5-digit constant is almost as long
as the number we want to represent, also
it is not interesting. So let's try other
multiples
RCL B ENTER ENTER ENTER + 36999.3456666
+ + + + + + + + + + + + + 277495.092497
... (very fast keystrokes, I may have missed
some interesting results)
+ + + + + + + + + + STO C 3625935.87485 the first four digits match those of
gamma(1/4)
4 1/x 1 - x! / 1000089.9067 now we have
(196/(gamma(1/4)*(10^6 + 90)) + sqrt(2) + 1)^3
= 14.0720129999
Again, not interesting enough, but after
noticing 196 = 14^2 and gamma(1/4) = (-0.75)!
we can try a pandigital expression. There are
repeated digits (0, 1 and 2) and 8 is missing.
Replacing 90 with 89 solves the latter and
eliminates one repeated 0, 1 can be written as
0! and 14^2 as Sq(14). Also Alog(x) can be used
for 10^x, so we finally have
(Sq(14)/((-.75)!*(Alog(6) + 89)) + Sqrt(2) + 0!)^3
14 ENTER * .75 +/- x! / 6 10x
89 + / 2 sqrt + 0 x! + 3 yx
DISP FIX 6 14.072013 = 14.0720130009
Go back to the main exhibit hall