A199219 Primes p, in the successive intervals (2^i +1 .. 2^(i+1) -1) such that p XOR 2^i -2 is composite for i=1,2,3...

23, 41, 47, 61, 67, 71, 73, 97, 101, 107, 127, 131, 137, 139, 149, 163, 167, 179, 181, 197, 199, 223, 229, 239, 241, 251, 257, 263, 271, 283, 293, 313, 317, 331, 353, 373, 383, 397, 433, 439, 443, 449, 463, 467, 479, 503, 509

Offset

1,1

Comments

The successive intervals (2^i +1 .. 2^(i+1) -1) are also (A000051(i)..A000225(i)). The value 2^i -2 XORed with the primes p in each interval is A000918(i). for i=1,2,3...

This is set of primes not in either A199217 or A199218.

The program provided produces output with primes in the successive intervals delimited by ****. For each interval, primes in the left half of interval are read from the top down, the right half of the interval primes from the bottom up.

Links

Table of n, a(n) for n=1..47.

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 [2 .. 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 not(IsPrime(xorcouple))) then j;
           end if;
        if (not(IsPrime(j)) and IsPrime(xorcouple)) then "  ", xorcouple;
           end if;
     end for;
     "****";
end for;

Crossrefs

Cf. A000051, A000225, A000918, A199217, A199218

Sequence in context: A227174 A050657 A050668 * A115699 A301623 A163635

Adjacent sequences: A199216 A199217 A199218 * A199220 A199221 A199222

Keyword

nonn

Author

Brad Clardy, Nov 04 2011

Status

approved