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%I #8 Nov 25 2023 00:08:24
%S 2,3,5,7,9,13,17,19,23,25,29,31,35,37,41,43,45,47,51,59,65,91,99,109,
%T 121,145,151,155,175,213,259,283,291,297,301,349,365,369,415,573,683,
%U 1017,1103,1195,1347,1537,1619,1717,1751,1957,2203,2431,2503,2653,2921
%N 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.
%C 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.
%C 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.
%e 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).
%Y Cf. A027856.
%K nonn
%O 1,1
%A _Jon E. Schoenfield_, Nov 24 2023