

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
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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
Index entries for sequences related to Goldbach conjecture
Index entries for sequences related to partitions


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*nq), 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



