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 A284928 Numbers k such that 2k + p is composite for all primes p, q with p + q = 2k. 2
 0, 1, 2, 3, 14, 19, 26, 29, 31, 34, 37, 40, 41, 44, 47, 49, 56, 59, 61, 62, 64, 68, 73, 74, 76, 79, 82, 83, 86, 89, 91, 92, 94, 95, 103, 104, 106, 107, 109, 110, 112, 119, 121, 122, 124, 125, 128, 131, 134, 139, 142, 145, 146, 148, 149, 151, 152, 154, 158, 160, 161, 163, 164, 166, 169 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Or, numbers k such that there is no prime p < 2k with 2k - p and 2k + p both prime. The two initial terms vacuously satisfy the definition, but all even numbers >= 4 are the sum of two primes, according to the Goldbach conjecture. See also A284919, twice this sequence, which lists the values of 2k. LINKS Claudio Meller and others, New sequence, SeqFan list, April 5, 2017. (Click "next" for subsequent contributions.) PROG (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 CROSSREFS Cf. A284919 (twice this), A002375 (number of decompositions p + q = 2k), A020481 (least p: p + q = 2k). Sequence in context: A212112 A107083 A266694 * A294405 A160218 A208983 Adjacent sequences:  A284925 A284926 A284927 * A284929 A284930 A284931 KEYWORD nonn AUTHOR M. F. Hasler, Apr 06 2017 STATUS approved

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Last modified June 26 00:12 EDT 2022. Contains 354870 sequences. (Running on oeis4.)