A361679 - OEIS

%I #15 Mar 20 2023 13:35:19

%S 3,3,5,3,7,11,3,5,13,17,5,7,11,19,29,3,11,13,23,37,41,3,7,29,31,29,43,

%T 59,7,11,19,41,37,53,67,71,11,13,23,37,47,43,59,79,101,7,29,37,29,43,

%U 71,67,71,97,107,5,37,59,61,53,67,107,73,89,103,137

%N A(n,k) is the n-th prime p such that p + 2^k is also prime; square array A(n,k), n>=1, k>=1, read by antidiagonals.

%H Alois P. Heinz, <a href="/A361679/b361679.txt">Antidiagonals n = 1..200, flattened</a>

%e Square array A(n,k) begins:

%e     3,   3,   3,   3,   5,   3,   3,   7,  11,   7, ...

%e     5,   7,   5,   7,  11,   7,  11,  13,  29,  37, ...

%e    11,  13,  11,  13,  29,  19,  23,  37,  59,  67, ...

%e    17,  19,  23,  31,  41,  37,  29,  61,  89,  73, ...

%e    29,  37,  29,  37,  47,  43,  53,  97, 101,  79, ...

%e    41,  43,  53,  43,  71,  67,  71, 103, 107, 127, ...

%e    59,  67,  59,  67, 107,  73,  83, 127, 131, 139, ...

%e    71,  79,  71,  73, 131, 103, 101, 163, 149, 157, ...

%e   101,  97,  89,  97, 149, 109, 113, 193, 179, 163, ...

%e   107, 103, 101, 151, 167, 127, 149, 211, 197, 193, ...

%p A:= proc() option remember; local f; f:= proc() [] end;

%p       proc(n, k) option remember; local p;

%p         p:= `if`(nops(f(k))=0, 1, f(k)[-1]);

%p         while nops(f(k))<n do p:= nextprime(p);

%p           if isprime(p+2^k) then f(k):= [f(k)[], p] fi

%p         od; f(k)[n]

%p       end

%p     end():

%p seq(seq(A(n, 1+d-n), n=1..d), d=1..12);

%Y Columns k=1-10 give: A001359, A023200, A023202, A049488, A049489, A049490, A049491, A361483, A361484, A361485.

%Y Row n=1 gives A056206.

%Y Main diagonal gives A361680.

%Y Cf. A000040.

%K nonn,look,tabl

%O 1,1

%A _Alois P. Heinz_, Mar 20 2023