

A112823


Greatest p less than or equal to n with p and q both prime, p+q = 2n.


10



2, 3, 3, 5, 5, 7, 5, 7, 7, 11, 11, 13, 11, 13, 13, 17, 17, 19, 17, 19, 13, 23, 19, 19, 23, 23, 19, 29, 29, 31, 23, 29, 31, 29, 31, 37, 29, 37, 37, 41, 41, 43, 41, 43, 31, 47, 43, 37, 47, 43, 43, 53, 47, 43, 53, 53, 43, 59, 59, 61, 53, 59, 61, 59, 61, 67, 53, 67, 67, 71, 71, 73
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OFFSET

2,1


COMMENTS

Essentially the same as A002374, which is the main entry for this sequence.  Franklin T. AdamsWatters, Jan 25 2010
Well defined only under the assumption that the yet unproved Goldbach conjecture holds, which states that any even N = 2n > 2 has a decomposition as sum of two primes.  M. F. Hasler, May 03 2019


LINKS

Table of n, a(n) for n=2..73.


FORMULA

a(n) = n  A047160(n).  Jason Kimberley, Aug 31 2011
a(n) = n if and only if n is prime, i.e., n in A000040.  M. F. Hasler, May 03 2019


EXAMPLE

From M. F. Hasler, May 03 2019: (Start)
For n = 2, the largest prime p <= n is p = 2, and q := 2n  p = 4  2 = 2 is also prime, whence a(2) = 2. We see that whenever n is prime, we will have a(n) = p = q = n.
For n = 4, the largest prime p <= n is p = 3, and q := 2n  p = 8  3 = 5 is also prime, whence a(4) = p = 3.
For n = 8, the largest prime less than n is p' = 7, but 2n  p' = 16  7 = 9 is not prime, so we have to go to the next smaller prime p = 5 and now q := 2n  p = 16  5 = 11 is also prime, whence a(8) = p = 5. (End)


MATHEMATICA

f[n_] := Block[{p = n/2}, While[ !PrimeQ[p]  !PrimeQ[n  p], p ]; p]; Table[ f[n], {n, 4, 146, 2}]


PROG

(PARI) a(n) = {my(p = precprime(n)); while (!isprime(2*np), p = precprime(p1)); p; } \\ Michel Marcus, Oct 22 2016
(PARI) A112823(n)=forprime(q=n, 2*n, isprime(2*nq)&&return(2*nq)) \\ M. F. Hasler, May 03 2019


CROSSREFS

Cf. A002374, A020481, A047160.
Sequence in context: A167411 A340195 A340192 * A247176 A325163 A348538
Adjacent sequences: A112820 A112821 A112822 * A112824 A112825 A112826


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, Sep 05 2005


STATUS

approved



