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A284928 Numbers k such that 2k + p is composite for all primes p, q with p + q = 2k. 2

%I

%S 0,1,2,3,14,19,26,29,31,34,37,40,41,44,47,49,56,59,61,62,64,68,73,74,

%T 76,79,82,83,86,89,91,92,94,95,103,104,106,107,109,110,112,119,121,

%U 122,124,125,128,131,134,139,142,145,146,148,149,151,152,154,158,160,161,163,164,166,169

%N Numbers k such that 2k + p is composite for all primes p, q with p + q = 2k.

%C Or, numbers k such that there is no prime p < 2k with 2k - p and 2k + p both prime.

%C The two initial terms vacuously satisfy the definition, but all even numbers >= 4 are the sum of two primes, according to the Goldbach conjecture.

%C See also A284919, twice this sequence, which lists the values of 2k.

%H Claudio Meller and others, <a href="http://list.seqfan.eu/pipermail/seqfan/2017-April/017433.html">New sequence</a>, SeqFan list, April 5, 2017. (Click "next" for subsequent contributions.)

%o (PARI) is_A284928(n)=!forprime(p=2,n, isprime(2*n-p) && (isprime(2*n+p) || isprime(4*n-p)) && return) \\ _M. F. Hasler_, Apr 06 2017

%Y Cf. A284919 (twice this), A002375 (number of decompositions p + q = 2k), A020481 (least p: p + q = 2k).

%K nonn

%O 1,3

%A _M. F. Hasler_, Apr 06 2017

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Last modified August 8 09:40 EDT 2022. Contains 356009 sequences. (Running on oeis4.)