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%I #15 Sep 08 2022 08:46:17
%S 3,5,17,257,8209,59141,65537,649801
%N Primes p such that (4^(p-1)-1) == 0 mod ((p-1)^2+1).
%C Prime terms from A273870.
%C The first 5 known Fermat primes from A019434 are in this sequence.
%C Conjecture 1: also primes p such that ((4^k)^(p-1)-1) == 0 mod ((p-1)^2+1) for all k >= 0.
%C Conjecture 2: supersequence of Fermat primes (A019434).
%e 5 is a term because (4^(5-1)-1) == 0 mod ((5-1)^2+1); 255 == 0 mod 17.
%o (Magma) [n: n in [1..100000] | IsPrime(n) and (4^(n-1)-1) mod ((n-1)^2+1) eq 0]
%o (PARI) is(n)=isprime(n) && Mod(4,(n-1)^2+1)^(n-1)==1 \\ _Charles R Greathouse IV_, Jun 08 2016
%Y Cf. A019434, A273870.
%K nonn,more
%O 1,1
%A _Jaroslav Krizek_, Jun 01 2016
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