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A361680 The n-th prime p such that p + 2^n is also prime.

%I A361680 #10 Mar 22 2023 08:17:16
%S A361680 3,7,11,31,47,67,83,163,179,193,263,367,389,499,563,571,887,967,1229,
%T A361680 1087,1367,1873,1289,2647,1907,2083,1979,2557,2267,3697,2909,3121,
%U A361680 3761,4507,4373,4723,5279,5857,6359,6793,7727,8167,7853,6823,6779,8059,9479,10567
%N A361680 The n-th prime p such that p + 2^n is also prime.
%C A361680 This sequence is non-monotonic: a(19) = 1229 > a(20) = 1087.
%H A361680 Alois P. Heinz, <a href="/A361680/b361680.txt">Table of n, a(n) for n = 1..1000</a>
%F A361680 a(n) = A361679(n,n).
%p A361680 b:= proc() option remember; local f; f:= proc() [] end;
%p A361680       proc(n, k) option remember; local p;
%p A361680         p:= `if`(nops(f(k))=0, 1, f(k)[-1]);
%p A361680         while nops(f(k))<n do p:= nextprime(p);
%p A361680           if isprime(p+2^k) then f(k):= [f(k)[], p] fi
%p A361680         od; f(k)[n]
%p A361680       end
%p A361680     end():
%p A361680 a:= n-> b(n$2):
%p A361680 seq(a(n), n=1..55);
%Y A361680 Main diagonal of A361679.
%Y A361680 Cf. A000040.
%K A361680 nonn
%O A361680 1,1
%A A361680 _Alois P. Heinz_, Mar 20 2023