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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.

A268209 Numbers n of the form 2^k + 1 such that n - k is a prime q (for k >= 0).

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%I A268209 #15 Sep 08 2022 08:46:15
%S A268209 2,3,5,17,65,65537,262145,18014398509481985,288230376151711745,
%T A268209 1267650600228229401496703205377,1329227995784915872903807060280344577
%N A268209 Numbers n of the form 2^k + 1 such that n - k is a prime q (for k >= 0).
%C A268209 Subsequence of A000051.
%C A268209 Prime terms are in A268210: 2, 3, 5, 17, 65537, ...
%C A268209 Corresponding values of numbers k are in A100361 (numbers n such that 2^n-n+1 is prime).
%C A268209 Corresponding values of primes q are in A100362 (primes of the form 2^n-n+1).
%C A268209 4 out of 5 known Fermat primes (3, 5, 17, 65537) are terms; corresponding values of primes q: 2, 3, 13, 65521.
%H A268209 Jaroslav Krizek, <a href="/A268209/b268209.txt">Table of n, a(n) for n = 1..12</a>
%F A268209 a(n) = A100362(n) + A100361(n).
%e A268209 17 = 2^4 + 1 is a term because 17 - 4 = 13 (prime).
%e A268209 257 = 2^8 + 1 is not a term because 257 - 8 = 249 (composite number).
%t A268209 2^# + 1 &@ Select[Range[0, 600], PrimeQ[2^# - # + 1] &] (* _Michael De Vlieger_, Jan 29 2016 *)
%o A268209 (Magma) [2^k + 1: k in [0..60] | IsPrime(2^k - k + 1)]
%Y A268209 Cf. A100361, A100362, A268210, A268211.
%K A268209 nonn
%O A268209 1,1
%A A268209 _Jaroslav Krizek_, Jan 28 2016