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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
Eric Weisstein's World of Mathematics, Goldbach Partition
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Dec 23 2013
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)