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 10^{x}

89 + / 2 sqrt + 0 *x*! + 3 *y*^{x}

DISP FIX 6 14.072013 = 14.0720130009

Calculator: HP-32SII

Shifts have been omitted in the keystrokes listing above