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A307782
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Even integers k such that there exists a prime p with p=min{q: q prime and (k-q) prime} and k < p^3.
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3
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4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 36, 38, 42, 48, 52, 54, 58, 60, 66, 68, 72, 78, 80, 84, 88, 90, 94, 96, 98, 102, 108, 114, 118, 120, 122, 124, 126, 128, 138, 146, 148, 150, 158, 164, 174, 180, 188, 190, 192, 206, 208, 210, 212, 218, 220, 222, 224, 240, 248, 250, 252, 258, 264, 270, 278, 290, 292, 294, 300, 302, 304, 306, 308, 324, 326, 328, 330, 332, 338, 346
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OFFSET
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1,1
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COMMENTS
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[Please keep the larger data section as it shows where the sequence first differs from A093161.]
This is another member of a family of sequences concerning the Strong Goldbach Conjecture, which I define as follows: Let (x, y, z) be real numbers with x >= 2, y > 0, z >= 0. An even integer k is then called an (x, y, z) Extraordinary Goldbach Number (EGN) if there exists a prime p with p=min{q: q prime and (k-q) prime} and (k - z*p) < y*p^x. a(n) represents the (3, 1, 0) extraordinary Goldbach numbers. A093161 consists of (3, 1, 1) EGN, A307542 are the (2, 1, 1) EGN, A279040 are the (2, 2, 0) EGN and A244408 are the (2, 1, 0).
a(104809) is very probably the last term and there are no more terms below 4*10^18.
There are only 11 terms in A093161 that are not in this sequence; these are 344, 1338, 12184, 12186, 24400, 148912, 1030342, 2571406, 3308008, 5929868, 15813352.
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LINKS
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Corinna Regina Böger, Table of n, a(n) for n = 1..10000
Corinna Regina Böger, a-file, Table of n, a(n) for n = 1..104809
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EXAMPLE
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344 is not in the sequence, because the smallest prime p for 344 is 7 with 7^3 = 343 < 344, whereas it is in A093161 due to 344 - 7 = 337 < 7^3.
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PROG
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(PARI) extraordinaryGoldbach(x, y, z, k) = forprime(p=2, k/2, if(isprime(k-p), if(y*p^x+z*p>=k, return(1), return(0)))); 0
is(n) = n%2 == 0 && extraordinaryGoldbach(3, 1, 0, n)
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CROSSREFS
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Cf. A093161, A244408, A279040, A307542.
Sequence in context: A163300 A193175 A093161 * A325038 A111305 A284665
Adjacent sequences: A307779 A307780 A307781 * A307783 A307784 A307785
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KEYWORD
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nonn
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AUTHOR
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Corinna Regina Böger, Apr 28 2019
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STATUS
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approved
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