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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


%S 23,41,47,61,67,71,73,97,101,107,127,131,137,139,149,163,167,179,181,

%T 197,199,223,229,239,241,251,257,263,271,283,293,313,317,331,353,373,

%U 383,397,433,439,443,449,463,467,479,503,509

%N 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...

%C 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...

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

%C 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.

%o (MAGMA)

%o XOR := func<a, b | Seqint([ (adigs[i] + bdigs[i]) mod 2 : i in [1..n]], 2)

%o where adigs := Intseq(a, 2, n)

%o where bdigs := Intseq(b, 2, n)

%o where n := 1 + Ilog2(Max([a, b, 1]))>;

%o for i in [2 .. 12] do

%o xornum:=2^(i)-2;

%o for j := 2^(i) +1 to 3*2^(i-1) by 2 do

%o xorcouple:=XOR(j,xornum);

%o if (IsPrime(j) and not(IsPrime(xorcouple))) then j;

%o end if;

%o if (not(IsPrime(j)) and IsPrime(xorcouple)) then " ",xorcouple;

%o end if;

%o end for;

%o "****";

%o end for;

%Y Cf. A000051, A000225, A000918, A199217, A199218

%K nonn

%O 1,1

%A _Brad Clardy_, Nov 04 2011

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Last modified October 15 17:58 EDT 2021. Contains 348033 sequences. (Running on oeis4.)