Happy Pi Day

[Leroy Quet]

Maximilian Hasler has been kind enough to extend
the sequence (and the table). The numbers he
calculated suggest another sequence:

a(n) is the smallest integer > a(n-1) such that
{pi^a(n)} < {pi^a(n-1)}, where {x} = x -
floor(x).
a(1)=1.

I get the sequence beginning: 1,3,81,...

Also interesting would be the sequence where:
a(n) = smallest integer > a(n-1) where pi^a(n) is
closer to an integer than pi^a(n-1). a(1)=1.

Anyone care to calculate these?
(Maximilian Hasler should probably have first
dibs on calculating this.)

Thanks,
Leroy Quet




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