A367630 Numbers k such that at least one 3-smooth number with k prime factors (counted with multiplicity) is the average of a twin prime pair.

2, 3, 5, 7, 9, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 45, 47, 51, 59, 65, 91, 99, 109, 121, 145, 151, 155, 175, 213, 259, 283, 291, 297, 301, 349, 365, 369, 415, 573, 683, 1017, 1103, 1195, 1347, 1537, 1619, 1717, 1751, 1957, 2203, 2431, 2503, 2653, 2921

Offset

1,1

Comments

Equivalently, numbers k for which there is at least one j such that 2^j * 3^(k-j) is the average of a twin prime pair.

The only even term is 2: the corresponding twin prime pairs are 2^2 * 3^0 -+ 1 = (3,5) and 2^1 * 3^1 -+ 1 = (5,7), each of which includes 5 as an element of the pair. If k is even, 2^j * 3^(k-j) differs by 1 from a multiple of 5 for every j.

Links

Table of n, a(n) for n=1..55.

Example

5 is a term: 2^3 * 3^2 = 8*9 = 72 is the average of a twin prime pair (and the same is true of 2^2 * 3^3 = 4*27 = 108).

Crossrefs

Cf. A027856.

Sequence in context: A028870 A338356 A057886 * A354531 A302835 A200672

Adjacent sequences: A367627 A367628 A367629 * A367631 A367632 A367633

Keyword

nonn

Author

Jon E. Schoenfield, Nov 24 2023

Status

approved