%I #14 Dec 16 2013 00:14:01

%S 1,2,1,2,3,2,3,4,3,1,2,3,2,3,1,2,3,2,3,2,3,4,3,4,2,3,4,3,4,2,3,4,3,4,

%T 3,1,2,3,2,3,4,3,4,5,1,2,3,2,3,4,2,3,4,1,2,3,2,3,4,2,3,4,1,2,3,2,3,4,

%U 2,3,4,2,2,3,3,3,4,2,3,4,2,3,3,3

%N Minimal number of c-squares (A020330) and/or 1's which add to n.

%C Conjecture: the sequence is bounded by a constant.

%e For n=33, we have 33=15+15+3. Since 33 is not in union of {1} and c-squares and is not a sum of two such numbers, then a(33)=3.

%o (PARI) v=vector(10^5,n,n+n<<#binary(n)); \\ choose large enough that v[#v] > n for a(n) below.

%o a(n)=if(setsearch(v,n),return(1));if(n<3,return(n));my(where=setsearch(v,n+1,1),t=n);if(!where,where=setsearch(v,n,1));forstep(i=where-1,1,-1,t=min(w(n-v[i]),t); if(t==1,return(2))); t+1 \\ _Charles R Greathouse IV_, Dec 10 2013

%Y Cf. A020330, A233312.

%K nonn

%O 1,2

%A _Vladimir Shevelev_, Dec 09 2013