

A156284


From every interval (2^(m1), 2^m), m >= 3, we remove primes p for which 2^mp is a prime that was not removed for smaller values of m; the sequence gives all remaining odd primes.


8



3, 7, 11, 17, 19, 23, 31, 37, 43, 59, 67, 71, 73, 79, 83, 89, 101, 103, 107, 113, 127, 131, 137, 139, 151, 157, 163, 179, 181, 191, 193, 199, 211, 223, 227, 229, 241, 251, 257, 263, 269
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OFFSET

1,1


COMMENTS

Powers of 2 are not expressible as sums of two primes from this sequence. This is attained by a more economical algorithm than that for construction of A152451. If A(x) is the counting function for the terms a(n) <= x, then A(x) = pi(x)  O(x/(log^2(x)). It is known that the approximation of pi(x) by x/log(x) gives the remainder term as, at best, O(x/log^2(x)). Therefore beginning our process from m >= M (with arbitrarily large M), we obtain a sequence which essentially is indistinguishable from the sequence of all odd primes with the help of the approximation of pi(x) by x/log(x). Hence it is in principle impossible to prove the binary Goldbach conjecture by such an approximation of pi(x).


LINKS

Table of n, a(n) for n=1..41.


CROSSREFS

Cf. A002375, A152451, A156537.
Sequence in context: A065376 A130090 A136059 * A045419 A049098 A119992
Adjacent sequences: A156281 A156282 A156283 * A156285 A156286 A156287


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Feb 07 2009


STATUS

approved



