- The sequence of key-presses

increases the number in the display window by one. Thus, the sequence is equivalent to the increment key (operator) . This solution is based on the following formula.

Generally speaking, if we have the formula

we can always obtain

by reducing*x*with*f*(*x*)=*n*-1, in which is the inverse function of*f*. For example, the above solution is using the equation

There are such equations

and

Based on the equations (6) and (7), we obtain another solutions

and

The last sequence (9) is derived by (Kaneko, 1989). -
The following sequence of key-presses

provide us -operator (Kaneko, 1989), where*k*is the number of . Using (5) - (7), several decrement key-sequences are given by

and

which are based on

in equation (4), where is the inverse function of*g*. - If your function calculator has [
*e*] key which provide*e*=2.718281828..., is obtained by the number of a set of key-presses that is