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%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
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