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

1,7

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.

Links

Table of n, a(n) for n=1..87.

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

See A154257 for a better version.

Sequence in context: A364384 A322907 A071018 * A155114 A038572 A334667

Adjacent sequences: A144556 A144557 A144558 * A144560 A144561 A144562

Keyword

nonn

Author

N. J. A. Sloane, Jan 03 2009

Status

approved