A226857 Numbers that are both the sum of two Fibonacci numbers and the product of two Fibonacci numbers.

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 15, 16, 21, 24, 26, 34, 39, 42, 55, 63, 68, 89, 102, 110, 144, 165, 178, 233, 267, 288, 377, 432, 466, 610, 699, 754, 987, 1131, 1220, 1597, 1830, 1974, 2584, 2961, 3194, 4181, 4791, 5168, 6765, 7752, 8362, 10946, 12543, 13530

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

Cf. A059389, A049997.

Sequence in context: A193299 A022773 A049997 * A256007 A324689 A280578

Adjacent sequences: A226854 A226855 A226856 * A226858 A226859 A226860

Keyword

nonn,easy

Author

Alonso del Arte, Jun 19 2013

Status

approved