

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
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OFFSET

1,1


COMMENTS

We iteratively scan integer intervals (2^(m1)..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^mk, 2^(m1) < 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^mk ;
if p <= 2^(m1) 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



