This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A367630 #8 Nov 25 2023 00:08:24 %S A367630 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 A367630 121,145,151,155,175,213,259,283,291,297,301,349,365,369,415,573,683, %U A367630 1017,1103,1195,1347,1537,1619,1717,1751,1957,2203,2431,2503,2653,2921 %N 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. %C A367630 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 A367630 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 A367630 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 A367630 Cf. A027856. %K A367630 nonn %O A367630 1,1 %A A367630 _Jon E. Schoenfield_, Nov 24 2023