Parity of number of partitions of an integer

[benoit]

Letting :

f(n) = A071640(n) = card( k <=n : p(k) odd)  (cf. also A087177=n+1-f(n))

In several papers there is the conjecture about : lim n-->infty  f(n)/n  
=  1/2

g(n)=2*f(n)-n is :

1,0,1,2,3,4,5,4,3,2,1,2,3,4,3,4,5,6,5,6,5,4,5,6,5,4,3,2,3,2,1,2,3,2,3,4, 
5,6,7,6,7,6,7,8,7,6,5,6,7,6,7,8,9,10,9,10,9,8,7,8,9,8,9,8,7,6,7,8,9,8,9, 
10,11,10,9,10,11,10,9,8,9,10,11,10,11,10,11,12,13,14,15,16,17,16,17,16,1 
5,14,15  (Not in EIS.)

I asked in A071640 whether  g(n) >=0 for all n...  Just checked for  
small values of n.

Benoit Cloitre






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