[seqfan] observation about A003160 a(1)=a(2)=1, a(n)=n-a(a(n-1))-a(a(n-2))

[Joerg Arndt]

Compute A003160:
? N=100; v=vector(N); v[1]=v[2]=1;
? for(n=3,N,v[n]=n-v[v[n-1]]-v[v[n-2]]); v
  [1, 1, 1, 2, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, ...]

Positions where seq increases:
? for(n=2,N,if(v[n]-v[n-1]>0,print1(n,", ")))
  4, 5, 6, 9, 12, 15, 16, 17, 20, 21, 22, 25, 26, ...

This appears to be A003156 (except initial term 1):
 a(n) is the number of ones before the n-th zero in
 the Feigenbaum sequence A035263. 

Initial term is obtained if we prepend a zero at the
beginning of A003160