OFFSET
1,3
COMMENTS
All Fibonacci numbers are in the sequence. The only prime numbers in this sequence are prime Fibonacci numbers.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
FORMULA
Conjecture: a(n) = a(n-3)+a(n-6) for n>12. - Colin Barker, Nov 09 2014
Empirical g.f.: -x^2*(x^10 +x^9 +x^8 +2*x^7 +3*x^6 +3*x^5 +3*x^4 +3*x^3 +3*x^2 +2*x +1) / (x^6 +x^3 -1). - Colin Barker, Nov 09 2014
EXAMPLE
5 + 21 = 2 * 13 = 26, therefore 26 is in the sequence.
8 + 21 = 1 * 34 = 34, therefore 34 is in the sequence.
5 + 34 = 3 * 13 = 39, therefore 39 is in the sequence.
MATHEMATICA
t = Fibonacci[Range[0, 25]]; t1 = Select[Union[Flatten[Table[a + b, {a, t}, {b, t}]]], # <= t[[-1]] &]; t2 = Select[Union[Flatten[Table[a*b, {a, t}, {b, t}]]], # <= t[[-1]] &]; Intersection[t1, t2] (* T. D. Noe, Jul 03 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alonso del Arte, Jun 19 2013
STATUS
approved