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A233420
Minimal number of c-squares (A020330) and/or 1's which add to n.
3
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, 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, 2, 3, 4, 2, 2, 3, 3, 3, 4, 2, 3, 4, 2, 3, 3, 3
OFFSET
1,2
COMMENTS
Conjecture: the sequence is bounded by a constant.
EXAMPLE
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.
PROG
(PARI) v=vector(10^5, n, n+n<<#binary(n)); \\ choose large enough that v[#v] > n for a(n) below.
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
CROSSREFS
Sequence in context: A359361 A033667 A033923 * A220098 A246017 A116939
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Dec 09 2013
STATUS
approved