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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.
0
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.
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
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Nov 24 2023
STATUS
approved