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A333958 The number of closed lambda calculus terms of size n that have a normal form, where size(lambda M)=2+size(M), size(M N)=2+size(M)+size(N), and size(V)=1+i for a variable V bound by the i-th enclosing lambda. 1

%I #21 Apr 18 2021 07:59:26

%S 0,0,0,1,0,1,1,2,1,6,5,13,14,37,44,101,134,297,431,882,1361,2729,4404,

%T 8548,14310,27397,47095,89014,156049,292954,521639,975319,1757422,

%U 3277997,5960021,11109379

%N The number of closed lambda calculus terms of size n that have a normal form, where size(lambda M)=2+size(M), size(M N)=2+size(M)+size(N), and size(V)=1+i for a variable V bound by the i-th enclosing lambda.

%C This sequence is uncomputable, like the corresponding Busy Beaver sequence A333479, which takes the maximum normal form size of the a(n) terms that have one.

%H Computed by changing "maximum $ (n,0,P Bot) :" in the main function of this <a href="https://github.com/tromp/AIT/blob/master/BB.lhs">Haskell program for analyzing Busy Beaver numbers</a> to "length".

%e This sequence first differs from A114852 at n=18 where it excludes the shortest term without a normal form (lambda x. x x)(lambda x. x x), hence a(18) = 298-1 = 297.

%Y Cf. A114852, A195691, A333479, A004147.

%K nonn,more

%O 1,8

%A _John Tromp_, Apr 22 2020

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Last modified April 19 07:26 EDT 2024. Contains 371782 sequences. (Running on oeis4.)