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Search: id:A156284
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| A156284 |
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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. |
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8
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| 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
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1,1
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COMMENT
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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).
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CROSSREFS
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A002375 A152451 A156537
Sequence in context: A065376 A130090 A136059 this_sequence A045419 A049098 A119992
Adjacent sequences: A156281 A156282 A156283 this_sequence A156285 A156286 A156287
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev (shevelev(AT)bgu.ac.il), Feb 07 2009
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