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A334092 Primes p of the form of the form q*2^h + 1, where q is one of the Fermat primes; Primes p for which A329697(p) == 2.

%I A334092 #24 Apr 20 2020 00:28:33
%S A334092 7,11,13,41,97,137,193,641,769,12289,40961,163841,557057,786433,
%T A334092 167772161,2281701377,3221225473,206158430209,2748779069441,
%U A334092 6597069766657,38280596832649217,180143985094819841,221360928884514619393,188894659314785808547841,193428131138340667952988161
%N A334092 Primes p of the form of the form q*2^h + 1, where q is one of the Fermat primes; Primes p for which A329697(p) == 2.
%C A334092 Primes p such that p-1 is not a power of two, but for which A171462(p-1) = (p-1-A052126(p-1)) is [a power of 2].
%C A334092 Primes of the form ((2^(2^k))+1)*2^h + 1, where ((2^(2^k))+1) is one of the Fermat primes, A019434, 3, 5, 17, 257, ..., .
%H A334092 Charles R Greathouse IV, <a href="/A334092/b334092.txt">Table of n, a(n) for n = 1..53</a>
%o A334092 (PARI) isA334092(n) = (isprime(n)&&2==A329697(n));
%o A334092 (PARI)
%o A334092 A052126(n) = if(1==n,n,n/vecmax(factor(n)[, 1]));
%o A334092 A209229(n) = (n && !bitand(n,n-1));
%o A334092 isA334092(n) = (isprime(n)&&(!A209229(n-1))&&A209229(n-1-A052126(n-1)));
%o A334092 (PARI) list(lim)=if(exponent(lim\=1)>=2^33, error("Verify composite character of more Fermat primes before checking this high")); my(v=List(),t); for(e=0,4, t=2^2^e+1; while((t<<=1)<lim, if(isprime(t+1), listput(v,t+1)))); Set(v) \\ _Charles R Greathouse IV_, Apr 14 2020
%Y A334092 Primes in A334102.
%Y A334092 Intersection of A081091 and A147545.
%Y A334092 Subsequences: A039687, A050526, A300407.
%Y A334092 Cf. A000040, A010051, A019434, A052126, A171462, A329697. Cf. also A334093, A334094, A334095, A334096.
%K A334092 nonn
%O A334092 1,1
%A A334092 _Antti Karttunen_, Apr 14 2020
%E A334092 More terms from _Giovanni Resta_, Apr 14 2020