

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...


0



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
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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...
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



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^(i1) 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



KEYWORD

nonn


AUTHOR



STATUS

approved



