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Primes of the form Phi(phi(k),2), the phi(k)-th cyclotomic polynomial evaluated at 2, where phi is the Euler totient function.
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%I #24 Aug 22 2019 12:03:24

%S 3,5,11,13,17,241,257,331,683,5419,61681,65537,2796203,15790321,

%T 22366891,4278255361,4562284561,77158673929,1133836730401,

%U 18446744069414584321,291280009243618888211558641,78919881726271091143763623681,84159375948762099254554456081,84179842077657862011867889681

%N Primes of the form Phi(phi(k),2), the phi(k)-th cyclotomic polynomial evaluated at 2, where phi is the Euler totient function.

%t s = Union[Table[EulerPhi[n], {n, 2000}]]; t = Union[Select[Table[ Cyclotomic[ n, 2], {n, s}], PrimeQ]]; Select[t, # < 10^30 &]

%o (PARI)

%o s=Set([]);

%o for (n=1,10^3, my(a=polcyclo(eulerphi(n),2)); if(ispseudoprime(a), s=setunion(s,[a])));

%o v211876=s /* _Joerg Arndt_, Apr 13 2013 */

%Y Cf. A000010, A211875, A211874.

%K nonn

%O 1,1

%A _Alexander Gruber_, Feb 12 2013