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A234345 Smallest q such that n <= q < 2n with p, q both prime, p+q = 2n, and p <= q.

%I A234345 #26 Feb 16 2025 08:33:21
%S A234345 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,
%T A234345 31,37,29,31,31,41,37,37,41,41,37,47,41,43,41,43,43,47,47,61,47,53,61,
%U A234345 53,59,61,53,61,67,59,61,73,59,61,61,71,67,67,71,71,67,83,71,73,71,73,73
%N A234345 Smallest q such that n <= q < 2n with p, q both prime, p+q = 2n, and p <= q.
%C A234345 Also, the larger part in the Goldbach partition of 2n with the smallest difference between its prime parts.
%H A234345 Vincenzo Librandi, <a href="/A234345/b234345.txt">Table of n, a(n) for n = 2..1000</a>
%H A234345 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A234345 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A234345 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A234345 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A234345 a(n) = 2n - A112823(n).
%e A234345 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.
%t A234345 f[n_] := Block[{p = n/2}, While[! PrimeQ[p] || ! PrimeQ[n - p], p--];
%t A234345   n - p]; Table[f[n], {n, 4, 146, 2}]
%o A234345 (PARI) a(n) = {my(q = nextprime(n)); while (!isprime(2*n-q), q = nextprime(q+1)); q;} \\ _Michel Marcus_, Oct 22 2016
%Y A234345 Cf. A112823.
%K A234345 nonn,easy
%O A234345 2,1
%A A234345 _Wesley Ivan Hurt_, Dec 23 2013