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A158846 Primes which are removed with the algorithm of A156284, starting the selection with the interval (2^4, 2^5). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..49.

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

CROSSREFS

Cf. A156284, A158756, A156759.

Sequence in context: A329106 A109276 A133765 * A157026 A240724 A274849

Adjacent sequences:  A158843 A158844 A158845 * A158847 A158848 A158849

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Mar 28 2009

STATUS

approved

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Last modified February 26 20:23 EST 2020. Contains 332295 sequences. (Running on oeis4.)