

A152461


Primes p such that there does not exist any positive integer k and prime q with p > q and 3^k = p + 2q or 3^k = q + 2p.


1



2, 7, 19, 41, 53, 61, 73, 79, 83, 89, 127, 131, 139, 151, 163, 167, 173, 179, 191, 193, 199, 211, 223, 227, 241, 257, 277, 293, 317, 337, 373, 379, 389, 397, 401, 409, 419, 421, 433, 439, 443, 449, 457, 461, 463, 479, 487, 491, 499
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OFFSET

1,1


COMMENTS

Powers of 3 are not expressible by sums of the form p + 2q, where p, q are terms of this sequence.
If there exists a sequence N_k = 3^n_k such that N_k has O((N_k)^v), v < 1/2, representations of the considered form, then removing the maximal primes in every such representation, we obtain an analog B of A152461 with the counting function Z(x) = pi(x)  O(x^v). Replacing in B the first N terms with N consecutive primes (with arbitrarily large N), we obtain a sequence which essentially is indistinguishable from the sequence of all primes with the help of the approximation of pi(x) by li(x), since, according to the wellknown Littlewood result, the remainder term in the theorem of primes cannot be less than sqrt(x)logloglog(x)/log(x). But for this sequence we have infinitely many odd numbers which are not expressible by sum p + 2q with p, q primes. Thus in this case the LemoineLevy conjecture is essentially unprovable. Nevertheless, we conjecture that there does not exist a considered abnormal case of sequence (N_k).


LINKS

Table of n, a(n) for n=1..49.


FORMULA

If A(X) is the counting function of the terms a(n) <= x, then A(x) = x/log(x) + O(x*log(log(x))/(log(x))^2).


CROSSREFS

Cf. A152460 (complement).
Sequence in context: A308269 A038562 A140610 * A215208 A100119 A322385
Adjacent sequences: A152458 A152459 A152460 * A152462 A152463 A152464


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Dec 05 2008, Dec 12 2008


STATUS

approved



