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 A234345 Smallest q such that n <= q < 2n with p, q both prime, p+q = 2n, and p <= q. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Also, the larger part in the Goldbach partition of 2n with the smallest difference between its prime parts. LINKS Vincenzo Librandi, Table of n, a(n) for n = 2..1000 Eric Weisstein's World of Mathematics, Goldbach Partition Wikipedia, Goldbach's conjecture FORMULA a(n) = 2n - A112823(n). EXAMPLE 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. MATHEMATICA f[n_] := Block[{p = n/2}, While[! PrimeQ[p] || ! PrimeQ[n - p], p--];   n - p]; Table[f[n], {n, 4, 146, 2}] PROG (PARI) a(n) = {my(q = nextprime(n)); while (!isprime(2*n-q), q = nextprime(q+1)); q; } \\ Michel Marcus, Oct 22 2016 CROSSREFS Cf. A112823. Sequence in context: A268101 A123318 A186698 * A111060 A082432 A336298 Adjacent sequences:  A234342 A234343 A234344 * A234346 A234347 A234348 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Dec 23 2013 STATUS approved

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Last modified April 22 22:19 EDT 2021. Contains 343197 sequences. (Running on oeis4.)