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 A268210 #17 Apr 30 2025 14:46:28 %S A268210 2,3,5,17,65537 %N A268210 Primes p of the form 2^k + 1 such that p - k is a prime q (for k >= 0). %C A268210 Intersection of A092506 and A268209. %C A268210 Sequence is not the same as A004249 because A004249(5) is a composite number. %C A268210 Corresponding values of numbers k: 0, 1, 2, 4, 16; corresponding values of primes q: 2, 2, 3, 13, 65521. %C A268210 4 out of 5 known Fermat primes from A019434 (3, 5, 17, 65537) are terms. %e A268210 Prime 17 = 2^4 + 1 is a term because 17 - 4 = 13 (prime). %e A268210 257 = 2^8 + 1 is not a term because 257 - 8 = 249 (composite number). %t A268210 2^# + 1 &@ Select[Range[0, 600], PrimeQ[2^# + 1] && PrimeQ[2^# - # + 1] &] (* _Michael De Vlieger_, Jan 29 2016 *) %o A268210 (Magma) [2^k + 1: k in [0..60] | IsPrime(2^k + 1) and IsPrime(2^k - k + 1)]; %Y A268210 Cf. A004249, A019434, A092506, A100361, A100362, A268209. %K A268210 nonn %O A268210 1,1 %A A268210 _Jaroslav Krizek_, Jan 28 2016