A228523 Numbers that are not the product of two Fibonacci numbers (not necessarily distinct).

7, 11, 12, 14, 17, 18, 19, 20, 22, 23, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92

Offset: 1

Author

Alonso del Arte, Sep 02 2013

Keywords

• nonn
• easy

Comments

All primes except prime Fibonacci numbers are in this sequence.

Examples

			Although 12 can be expressed as a product of Fibonacci numbers, it takes three of them, not two, hence 12 is in the list.
There is no way to express 14 as a product of Fibonacci numbers since its larger prime factor, 7, is not a Fibonacci number, hence 14 is in the list.
16 is not in the list because it can be expressed as 2 * 8.
		

Crossrefs

Cf. A049997 (complement).

Programs

Mathematica

nn = 12; f = Fibonacci[Range[2, nn]]; f2 = Select[Union[Flatten[Outer[Times, f, f]]], # <= f[[-1]] &]; Complement[Range[f[[-1]]], f2] (* T. D. Noe, Sep 03 2013 *)