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...

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

Links

Table of n, a(n) for n=1..51.

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

Cf. A000051, A000225, A000918, A007283, A199218.

Sequence in context: A191206 A191141 A268155 * A141165 A220954 A155937

Adjacent sequences: A199214 A199215 A199216 * A199218 A199219 A199220

Keyword

nonn

Author

Brad Clardy, Nov 04 2011

Status

approved