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%I #51 Aug 06 2021 01:57:29
%S 4,5,13,53,8645
%N Numbers k such that the k-th ménage number is prime.
%C This sequence is heuristically conjectured to grow doubly-exponentially.
%C a(6) > 100000. - _Hans Havermann_, Jan 19 2019
%H Adam P. Goucher, <a href="https://cp4space.wordpress.com/2014/10/31/menage-primes/">Menage primes</a>, Complex Projective 4-Space.
%e The only known ménage primes are M(4) = 2, M(5) = 13, M(13) = 775596313, M(53) = 567525075138663383127158192994765939404930668817780601409606090331861, and M(8645).
%o (PARI) is(n)=ispseudoprime(round(2*n*exp(-2)*besselk(n, 2))) \\ _Charles R Greathouse IV_, Nov 10 2014
%Y By definition, the inverse image of A000040 under the function A000179.
%Y The ménage primes themselves are given in A249510.
%K nonn,hard
%O 1,1
%A _Adam P. Goucher_, Oct 30 2014
%E Example edited by _Hans Havermann_, Jan 19 2019