cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A297625 Primes of the form (2^(p^k) - 1)/(2^(p^(k - 1)) - 1), with p prime and k > 1.

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%I A297625 #20 Sep 08 2022 08:46:20
%S A297625 5,17,73,257,65537,262657,4432676798593
%N A297625 Primes of the form (2^(p^k) - 1)/(2^(p^(k - 1)) - 1), with p prime and k > 1.
%C A297625 Primes of the form Phi(x, 2), where x is a proper prime power and Phi is the cyclotomic polynomial.
%C A297625 Together with 3, supersequence of A019434.
%C A297625 Also called Mersenne-Fermat primes.
%C A297625 a(8) has 1031 digits and is too large to include.
%D A297625 Fredrick Kennard, Unsolved Problems in Mathematics, Lulu Press, 2015, p. 160.
%H A297625 Wikipedia, <a href="https://en.wikipedia.org/wiki/Mersenne_prime#Mersenne%E2%80%93Fermat_primes">Mersenne-Fermat primes</a>
%o A297625 (Magma) lst:=[]; r:=7; pr:=PrimesUpTo(r); for k in [2..r] do for c in [1..#pr] do p:=pr[c]; if p^k le r^2 then MF:=Truncate((2^(p^k)-1)/(2^(p^(k-1))-1)); if IsPrime(MF) then Append(~lst, MF); end if; end if; end for; end for; Sort(lst);
%Y A297625 Cf. A019434, A051156, A140797, A187823, A245730, A246547.
%K A297625 nonn
%O A297625 1,1
%A A297625 _Arkadiusz Wesolowski_, Jan 04 2018