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

19, 29, 41, 47, 53, 59, 61, 97, 149, 167, 173, 233, 239, 251, 271, 283, 313, 331, 349, 373, 409, 433, 439, 499, 509, 521, 557, 563, 593, 641, 677, 743, 761, 797, 827, 887, 911, 941, 953, 1013, 1019, 1021, 1039, 1051, 1129, 1171, 1237, 1279, 1291

Offset: 1

Author

Vladimir Shevelev, Mar 28 2009

Keywords

• nonn

Comments

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.

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

Crossrefs

Cf. A156284, A158756, A156759.

Programs

Maple

A158846 := proc()
        local mmax,prrem,m,prm,pi,p,q ;
        mmax := 12 ; prrem := {} ;
        for m from 5 to mmax do
                prm := {} ;
                for pi from 1 do
                        k := ithprime(pi) ;
                        p := 2^m-k ;
                        if p <= 2^(m-1) then  break; end if;
                        if isprime(p) and not k in prrem then prm := prm union {p} ;
                        end if ;
                end do:
                prrem := prrem union prm ;
        end do: print( sort(prrem)) ; return ;
end proc:
A158846() ; # R. J. Mathar, Dec 07 2010