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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

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*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.)