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A158846 Primes which are removed with the algorithm of A156284, starting the selection with the interval (2^4, 2^5).

%I A158846 #8 May 12 2019 02:17:32
%S A158846 19,29,41,47,53,59,61,97,149,167,173,233,239,251,271,283,313,331,349,
%T A158846 373,409,433,439,499,509,521,557,563,593,641,677,743,761,797,827,887,
%U A158846 911,941,953,1013,1019,1021,1039,1051,1129,1171,1237,1279,1291
%N A158846 Primes which are removed with the algorithm of A156284, starting the selection with the interval (2^4, 2^5).
%C A158846 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 A158846 Powers 2^m, m >= 5, are not expressible as sums of two primes which are not in the sequence.
%p A158846 A158846 := proc()
%p A158846         local mmax,prrem,m,prm,pi,p,q ;
%p A158846         mmax := 12 ; prrem := {} ;
%p A158846         for m from 5 to mmax do
%p A158846                 prm := {} ;
%p A158846                 for pi from 1 do
%p A158846                         k := ithprime(pi) ;
%p A158846                         p := 2^m-k ;
%p A158846                         if p <= 2^(m-1) then  break; end if;
%p A158846                         if isprime(p) and not k in prrem then prm := prm union {p} ;
%p A158846                         end if ;
%p A158846                 end do:
%p A158846                 prrem := prrem union prm ;
%p A158846         end do: print( sort(prrem)) ; return ;
%p A158846 end proc:
%p A158846 A158846() ; # _R. J. Mathar_, Dec 07 2010
%Y A158846 Cf. A156284, A158756, A156759.
%K A158846 nonn
%O A158846 1,1
%A A158846 _Vladimir Shevelev_, Mar 28 2009