A144559 a(n) = number of triples [i,j,k] with i+j+k = n, i an odd prime, j an odd Fibonacci number and k a positive Fibonacci number.

0, 0, 0, 0, 1, 1, 3, 2, 6, 3, 7, 3, 7, 4, 6, 5, 8, 5, 10, 5, 12, 5, 10, 5, 12, 7, 13, 6, 15, 4, 12, 6, 13, 7, 13, 5, 16, 5, 13, 8, 11, 8, 11, 7, 17, 8, 15, 6, 12, 8, 11, 10, 13, 7, 13, 6, 12, 9, 12, 8, 14, 7, 19, 8, 18, 10, 16, 9, 15, 9, 16, 6, 16, 9, 19, 11, 18, 7, 19, 8, 16, 10, 14, 7, 18, 8, 21

Offset: 1

Author

N. J. A. Sloane, Jan 03 2009

Keywords

• nonn

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.

Examples

			5 = 3+1+1, 6 = 3+1+2, 7 = 5+1+1 = 3+3+1 = 3+1+3.
		

Crossrefs

See A154257 for a better version.

Programs

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)];