Some numbers, in order

[fivemack]

16
3+pi+pi^2
1+2*pi+2^pi
13+pi
2*pi+pi^2
2*pi+10
3*pi+7
4*pi+4
5*pi+1
2^pi+8
pi^2+7
pi+2^pi+5
17

This may make more sense to readers of alt.sysadmin.recovery. The idea is to list the elements of the smallest set containing 1 and pi, and closed under addition, multiplication and raising to powers.

http://www.chiark.greenend.org.uk/~twomack/gen_kylix2.cpp should let all my readers play about with this silly problem; note that floating-point precision means that you can't get to 20 before the computer fails to realise that

(pi+((1+(pi+pi))+((1+1)^pi)))

and

(((1+1)^pi)+((1+pi)+(pi+pi)))

should be equal