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%I #17 Sep 08 2022 08:46:00
%S 3,5,11,17,19,37,43,79,83,89,151,157,173,191,269,277,281,307,311,337,
%T 347,349,359,367,379,523,569,599,607,617,653,659,673,677,683,709,727,
%U 739,1033,1061,1069,1093,1123,1171,1193,1201,1249,1283,1289,1319,1373
%N Primes p in successive intervals (2^i+1 .. 3*2^(i-1)) such that p XOR (2^i -2) produces a prime q in the range (3*2^(i-1) .. 2^(i+1)-1) for i=1,2,3...
%C The successive intervals (2^i +1 .. 3*2^(i-1)) are also (A000051(i)..A007283(i-1)). The value 2^i -2 XORed with the prime p is A000918(i). The prime couples are in the intervals (A007283(i-1)..A000225(i)) for i=1,2,3...
%C The coupled terms are located in A199218 and share the same index value
%o (Magma)
%o XOR := func<a, b | Seqint([ (adigs[i] + bdigs[i]) mod 2 : i in [1..n]], 2)
%o where adigs := Intseq(a, 2, n)
%o where bdigs := Intseq(b, 2, n)
%o where n := 1 + Ilog2(Max([a, b, 1]))>;
%o for i in [1 .. 12] do
%o xornum:=2^(i)-2;
%o for j := 2^(i) +1 to 3*2^(i-1) by 2 do
%o xorcouple:=XOR(j,xornum);
%o if (IsPrime(j) and IsPrime(xorcouple)) then j;
%o end if;
%o end for;
%o "****";
%o end for;
%Y Cf. A000051, A000225, A000918, A007283, A199218.
%K nonn
%O 1,1
%A _Brad Clardy_, Nov 04 2011
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