|
| |
|
|
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; 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
|
|
|
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: A151360 A109276 A133765 * A157026 A108183 A157483
Adjacent sequences: A158843 A158844 A158845 * A158847 A158848 A158849
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Vladimir Shevelev (shevelev(AT)bgu.ac.il), Mar 28 2009
|
| |
|
|
