OFFSET
1,7
COMMENTS
Zhi-Wei Sun conjectured on the Number Theory Mailing List that a(n) > 0 for all n > 4.
The conjecture has been verified by D. S. McNeil for all n < 10^13.
EXAMPLE
5 = 3+1+1, 6 = 3+1+2, 7 = 5+1+1 = 3+3+1 = 3+1+3.
MAPLE
with(combinat); F:=fibonacci; ans:=array(1..100); oF:=[]; pF:=[];
for n from 1 to 100 do ans[n] := 0; od:
for n from 2 to 12 do if F(n) mod 2 = 1 then oF:=[op(oF), F(n)]; fi; od;
for n from 2 to 12 do pF:=[op(pF), F(n)]; od:
for i from 2 to 30 do t1:=ithprime(i);
for j from 1 to nops(oF) do t2:=t1+oF[j]:
for k from 1 to nops(pF) do t3:=t2+pF[k];
if t3 <= 100 then ans[t3]:=ans[t3]+1; fi;
od: od: od: [seq(ans[n], n=1..100)];
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 03 2009
STATUS
approved