A080309 n-th even number equals n-th multiple of a Fermat number.

3, 5, 6, 9, 10, 12, 15, 17, 24, 25, 27, 30, 33, 34, 39, 40, 42, 45, 48, 50, 51, 60, 63, 65, 66, 68, 69, 70, 72, 75, 78, 80, 81, 95, 96, 111, 119, 120, 123, 125, 126, 129, 130, 132, 135, 136, 144, 159, 160, 174, 175, 177, 180, 183, 185, 186, 187, 189, 190, 192, 195, 204

Offset: 1

Author

Matthew Vandermast, Feb 16 2003

Keywords

• nonn

Comments

Sequence includes only multiples of Fermat numbers (sequence A080307), but not all of them. It is not certain that A080309 is infinite, but it seems likely given that exactly one-half of all integers are multiples of Fermat numbers (see A080307).

Examples

			The first 3 even numbers are 2, 4 and 6; the first 3 multiples of Fermat numbers (the numbers of the form 2^(2^n)+1) are 3, 5 and 6. The third even number is also the third Fermat multiple; thus 3 is in the sequence.
		

Crossrefs

Cf. A000215 (the Fermat numbers), A080307.