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A199217
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...
2
3, 5, 11, 17, 19, 37, 43, 79, 83, 89, 151, 157, 173, 191, 269, 277, 281, 307, 311, 337, 347, 349, 359, 367, 379, 523, 569, 599, 607, 617, 653, 659, 673, 677, 683, 709, 727, 739, 1033, 1061, 1069, 1093, 1123, 1171, 1193, 1201, 1249, 1283, 1289, 1319, 1373
OFFSET
1,1
COMMENTS
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...
The coupled terms are located in A199218 and share the same index value
PROG
(Magma)
XOR := func<a, b | Seqint([ (adigs[i] + bdigs[i]) mod 2 : i in [1..n]], 2)
where adigs := Intseq(a, 2, n)
where bdigs := Intseq(b, 2, n)
where n := 1 + Ilog2(Max([a, b, 1]))>;
for i in [1 .. 12] do
xornum:=2^(i)-2;
for j := 2^(i) +1 to 3*2^(i-1) by 2 do
xorcouple:=XOR(j, xornum);
if (IsPrime(j) and IsPrime(xorcouple)) then j;
end if;
end for;
"****";
end for;
CROSSREFS
KEYWORD
nonn
AUTHOR
Brad Clardy, Nov 04 2011
STATUS
approved