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Some numbers, in order
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
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