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.
%I A065406 #33 Aug 23 2020 02:36:53 %S A065406 2,3,5,89,9689,21701,859433,43112609 %N A065406 Mersenne prime exponents (A000043) which are also Sophie Germain primes (A005384). %C A065406 From _Gord Palameta_, Jul 19 2018: (Start) %C A065406 All terms after the first two are congruent to 1 modulo 4, because if p is a Sophie Germain prime that is congruent to 3 modulo 4 then 2p + 1 divides 2^p - 1. %C A065406 Boklan and Conway conjecture that this sequence is finite. %C A065406 (End) %H A065406 David W. Ash, Ian F. Blake, and Scott A. Vanstone, <a href="https://doi.org/10.1016/0166-218X(89)90001-2">Low Complexity Normal Bases</a>, Discrete Applied Mathematics, 25(1989), 206. %H A065406 Kent D. Boklan, John H. Conway, <a href="https://arxiv.org/abs/1605.01371">Expect at most one billionth of a new Fermat Prime!</a>, arXiv:1605.01371 [math.NT], 2016, p. 6. %e A065406 31 = 2^5 - 1 and 11 = 2 * 5 + 1 are primes. %t A065406 Select[Prime[Range[1000]], PrimeQ[2# + 1] && PrimeQ[2^# - 1] &] (* _Alonso del Arte_, Jul 20 2018 *) %t A065406 Select[Prime@ Range[10^6], And[PrimeQ[2 # + 1], MersennePrimeExponentQ@ #] &] (* _Michael De Vlieger_, Jul 20 2018 *) %Y A065406 Cf. A000043, A005384. %K A065406 nonn,more %O A065406 1,1 %A A065406 _Labos Elemer_, Nov 06 2001 %E A065406 a(8) = 43112609, since the ordinal position of this term in A000043 is now confirmed. - _Gord Palameta_, Jul 19 2018