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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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A227174 A050657 A050668 * A115699 A301623 A163635
KEYWORD
nonn
AUTHOR
Brad Clardy, Nov 04 2011
STATUS
approved

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Last modified February 25 18:54 EST 2024. Contains 370332 sequences. (Running on oeis4.)