%I A156284
%S A156284 3,7,11,17,19,23,31,37,43,59,67,71,73,79,83,89,101,103,107,113,127,131,
%T A156284 137,139,151,157,163,179,181,191,193,199,211,223,227,229,241,251,257,
%U A156284 263,269
%N A156284 From every interval (2^(m-1), 2^m), m>=3, we remove primes p for which 
               2^m-p is a prime which was not removed for smaller values of m; the 
               sequence gives all remaining odd primes.
%C A156284 Powers of 2 are not expressible as sums of two primes from this sequence. 
               This attains by more economical algorithm than for construction of 
               A152451. If A(x) is the counting function for the terms a(n)<=x, 
               then A(x)=pi(x)-O(x/(ln^2(x)). It is known that the approximation 
               pi(x) by x/ln(x) gives the remainder term as best O(x/ln^2(x)). Therefore 
               beginning our process from m>=M (with arbitrary large M), we obtain 
               a sequence which essentially is indistinguishable from the sequence 
               of all odd primes with help of the approximation of pi(x) by x/lnx. 
               Hence it is in principle impossible to prove the binary Goldbach 
               conjecture by such approximation of pi(x).
%Y A156284 A002375 A152451 A156537
%Y A156284 Sequence in context: A065376 A130090 A136059 this_sequence A045419 A049098 
               A119992
%Y A156284 Adjacent sequences: A156281 A156282 A156283 this_sequence A156285 A156286 
               A156287
%K A156284 nonn
%O A156284 1,1
%A A156284 Vladimir Shevelev (shevelev(AT)bgu.ac.il), Feb 07 2009