cp's OEIS Frontend

Empirical: a(n)=a(n-1)+2*a(n-2)-a(n-3)-a(n-4)-a(n-5)+a(n-9)-a(n-10)+3*a(n-12)+a(n-13)-a(n-14)-a(n-16)-2*a(n-17)-a(n-18)-a(n-20)+a(n-22)+2*a(n-23)+2*a(n-24)+a(n-25)-a(n-27)-a(n-29)-2*a(n-30)-a(n-31)-a(n-33)+a(n-34)+3*a(n-35)-a(n-37)+a(n-38)-a(n-42)-a(n-43)-a(n-44)+2*a(n-45)+a(n-46)-a(n-47)

Empirical: a(n)=a(n-1)+2*a(n-2)-a(n-3)-a(n-4)-a(n-6)-2*a(n-7)+a(n-8)+2*a(n-9)+a(n-11)+2*a(n-12)-a(n-13)-a(n-14)+2*a(n-15)-a(n-16)-4*a(n-17)-3*a(n-20)+a(n-21)+3*a(n-22)+a(n-24)+4*a(n-25)-a(n-26)-a(n-27)+3*a(n-28)-a(n-29)-4*a(n-30)-4*a(n-33)-a(n-34)+3*a(n-35)-a(n-36)-a(n-37)+4*a(n-38)+a(n-39)+3*a(n-41)+a(n-42)-3*a(n-43)-4*a(n-46)-a(n-47)+2*a(n-48)-a(n-49)-a(n-50)+2*a(n-51)+a(n-52)+2*a(n-54)+a(n-55)-2*a(n-56)-a(n-57)-a(n-59)-a(n-60)+2*a(n-61)+a(n-62)-a(n-63)

a(n) = 2 if and only if n = 3 or n + 1 > 2 is prime (Hemmer and Westrem).

For proofs of the following, see A368548.

Let T(n,k) be the table in A183917.

Let x = 0 if n is even and x = Sum_{d|(n+1)/2} T((n+1)/d-2,d-1) if n is odd.

Let y = 2*Sum_{d|n+1, d>=3, and d is odd} T(d-2,(n+1)/d-1).

Then a(n) = x+y.

If n>3 is odd and (n+1)/2 is prime, then a(n) = A368548(n) = (n+3)/2.

a(2^n-1) = Sum_{i=0..n-1} T(2^(n-i)-2,2^i-1).