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%I #6 Jun 16 2019 22:31:52
%S 2,5,28,70,2,1820,110,1850,2520,220,2023,9415,647,2880,2562,3895,2,
%T 51240,525,3750,147,2350,355,4480,2588,3370,38157,1185,1473,12530,
%U 4338,1540,1988,535,102,22606,13773,18895,16373,2635,20428,76300,23037,29005,11078
%N Least k > 1 such that k^n is a twin rank (cf. A002822: 6*k^n +- 1 are twin primes).
%C Dinculescu observes that when k^2 > 1 is a twin rank (i.e., in A002822) then 5 | k (k is divisible by 5), and if k^3 is a twin rank, then 7 | k; cf. A326232 & A326234. It is unknown whether there are other pairs (a, b) such that a | n whenever n^b > 1 is a twin rank. (Of course 2 | b => 5 | a and 3 | b => 7 | a, so we aren't interested in pairs (a, b) which are consequence of this.)
%H A. Dinculescu, <a href="http://www.utgjiu.ro/math/sma/v13/p13_11.pdf">On the Numbers that Determine the Distribution of Twin Primes</a>, Surveys in Mathematics and its Applications, 13 (2018), 171-181.
%o (PARI) a(n)=for(k=2,oo,ispseudoprime(6*k^n-1)&&ispseudoprime(6*k^n+1)&&return(k))
%Y Cf. A326231 .. A326236, A002822.
%K nonn
%O 1,1
%A _M. F. Hasler_ and _Antonie Dinculescu_, Jun 16 2019