A156284 From every interval (2^(m-1), 2^m), m >= 3, we remove primes p for which 2^m-p is a prime that was not removed for smaller values of m; the sequence gives all remaining odd primes.

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

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