A080309 Numbers k such that the k-th positive even number equals the k-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

1,1

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).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The first 3 positive 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.

Maple

N:= 10^3: # for terms <= N
mm:= floor(fsolve(2^(2^m)+1=2*N)):
FM:= sort(convert({seq(seq(k, k=2^(2^m)+1 .. 2*N, 2^(2^m)+1), m=0..mm)}, list)):
select(t -> FM[t]=2*t, [$1..nops(FM)]); # Robert Israel, Feb 20 2026

Crossrefs

Cf. A000215 (the Fermat numbers), A005843, A080307, A299174.

Sequence in context: A075311 A392367 A032786 * A281746 A287162 A018900

Adjacent sequences: A080306 A080307 A080308 * A080310 A080311 A080312

Keyword

nonn

Author

Matthew Vandermast, Feb 16 2003

Status

approved