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

Author

Jon E. Schoenfield, Nov 24 2023

Keywords

• nonn

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.

Examples

			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.