%I #16 Nov 05 2023 21:07:05
%S 2,4,12,36,72,192,1152,2592,2916,1492992,1990656,5308416,28311552,
%T 6879707136,1761205026816,5566277615616,79164837199872,
%U 3799912185593856,115422332637413376,1332669751402954752,4803028329503971872
%N 3-smooth numbers k such that k+1 and (k+2)/2 are prime.
%C Numbers k of the form 2^a*3^b such that k+1 and (k+2)/2 are prime.
%C All terms except 2 and 4 are in A325204.
%C All terms except 4 end in 2 or 6.
%H Ray Chandler, <a href="/A325255/b325255.txt">Table of n, a(n) for n = 1..41</a> (terms < 10^1000; first 39 terms from Robert Israel)
%e a(3)=12 is a term because 12=2^2*3 and 13 and 14/2 are prime.
%p N:= 10^100: # to get terms <= N
%p sort(select(t -> isprime(t+1) and isprime((t+2)/2), [seq(seq(2^i*3^j, i = 1 .. ilog2(N/3^j)), j=0..floor(log[3](N)))]));
%Y Cf. A003586, A325204, A327240.
%K nonn
%O 1,1
%A _Robert Israel_, Sep 05 2019