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A234345
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Smallest q such that n <= q < 2n with p, q both prime, p+q = 2n, and p <= q.
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5
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2, 3, 5, 5, 7, 7, 11, 11, 13, 11, 13, 13, 17, 17, 19, 17, 19, 19, 23, 23, 31, 23, 29, 31, 29, 31, 37, 29, 31, 31, 41, 37, 37, 41, 41, 37, 47, 41, 43, 41, 43, 43, 47, 47, 61, 47, 53, 61, 53, 59, 61, 53, 61, 67, 59, 61, 73, 59, 61, 61, 71, 67, 67, 71, 71, 67, 83, 71, 73, 71, 73, 73
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OFFSET
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2,1
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COMMENTS
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Also, the larger part in the Goldbach partition of 2n with the smallest difference between its prime parts.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 2..1000
Eric Weisstein's World of Mathematics, Goldbach Partition
Wikipedia, Goldbach's conjecture
Index entries for sequences related to Goldbach conjecture
Index entries for sequences related to partitions
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FORMULA
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a(n) = 2n - A112823(n).
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EXAMPLE
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a(9) = 11; the Goldbach partitions of 2(9) = 18 are (13,5) and (11,7). The partition with smaller difference between the primes is (11,7) (difference 4) and the larger part of this partition is 11.
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MATHEMATICA
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f[n_] := Block[{p = n/2}, While[! PrimeQ[p] || ! PrimeQ[n - p], p--];
n - p]; Table[f[n], {n, 4, 146, 2}]
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PROG
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(PARI) a(n) = {my(q = nextprime(n)); while (!isprime(2*n-q), q = nextprime(q+1)); q; } \\ Michel Marcus, Oct 22 2016
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CROSSREFS
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Cf. A112823.
Sequence in context: A268101 A123318 A186698 * A111060 A082432 A336298
Adjacent sequences: A234342 A234343 A234344 * A234346 A234347 A234348
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KEYWORD
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nonn,easy
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AUTHOR
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Wesley Ivan Hurt, Dec 23 2013
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STATUS
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approved
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