A158846 - OEIS

%I #8 May 12 2019 02:17:32

%S 19,29,41,47,53,59,61,97,149,167,173,233,239,251,271,283,313,331,349,

%T 373,409,433,439,499,509,521,557,563,593,641,677,743,761,797,827,887,

%U 911,941,953,1013,1019,1021,1039,1051,1129,1171,1237,1279,1291

%N Primes which are removed with the algorithm of A156284, starting the selection with the interval (2^4, 2^5).

%C We iteratively scan integer intervals (2^(m-1)..2^m), first the one with m=5, then m=6, m=7, etc., and start with the set S={3,5,7,11,...} of all odd primes. For each prime p = 2^m-k, 2^(m-1) < p < 2^m, p is removed from S if k is in S. Basically, all the upper primes of primes pairs are removed when the prime pair sums to a power of 2 which are larger than 2^4. The sequence shows all p that are removed from S at any stage m.

%C Powers 2^m, m >= 5, are not expressible as sums of two primes which are not in the sequence.

%p A158846 := proc()

%p         local mmax,prrem,m,prm,pi,p,q ;

%p         mmax := 12 ; prrem := {} ;

%p         for m from 5 to mmax do

%p                 prm := {} ;

%p                 for pi from 1 do

%p                         k := ithprime(pi) ;

%p                         p := 2^m-k ;

%p                         if p <= 2^(m-1) then  break; end if;

%p                         if isprime(p) and not k in prrem then prm := prm union {p} ;

%p                         end if ;

%p                 end do:

%p                 prrem := prrem union prm ;

%p         end do: print( sort(prrem)) ; return ;

%p end proc:

%p A158846() ; # _R. J. Mathar_, Dec 07 2010

%Y Cf. A156284, A158756, A156759.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Mar 28 2009