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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 well-known 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 Lemoine-Levy conjecture is essentially unprovable. Nevertheless, we conjecture that there does not exist a considered abnormal case of sequence (N_k).