A002374 Largest prime <= n in any decomposition of 2n into a sum of two odd primes.

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, 59

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

Comments

Sequence A112823 is identical except that it is very naturally extended to a(2) = 2, i.e., the word "odd" is dropped from the definition. - M. F. Hasler, May 03 2019

References

• D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 80.
• N. Pipping, Neue Tafeln für das Goldbachsche Gesetz nebst Berichtigungen zu den Haussnerschen Tafeln, Finska Vetenskaps-Societeten, Comment. Physico Math. 4 (No. 4, 1927), pp. 1-27.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A002372, A002373, A014092, A234345.

Essentially the same as A112823. - Franklin T. Adams-Watters, Jan 25 2010

Programs

Mathematica

nmax = 74; a[n_] := (k = 0; While[k < n && (!PrimeQ[n-k] || !PrimeQ[n+k]), k++]; If[k == n, n+1, n-k]); Table[a[n], {n, 3, nmax}](* Jean-François Alcover, Nov 14 2011, after Jason Kimberley *)
lp2n[n_]:=Max[Select[Flatten[Select[IntegerPartitions[2n,{2}],AllTrue[ #, PrimeQ]&]],#<=n&]]; Array[lp2n,80,2] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 08 2018 *)

PARI

a(n)=forstep(k=n,1,-1, if(isprime(k) && isprime(2*n-k), return(k))) \\ Charles R Greathouse IV, Feb 07 2017

PARI

A002374(n)=forprime(q=n, 2*n, isprime(2*n-q)&&return(2*n-q)) \\ M. F. Hasler, May 03 2019

Formula

a(n) = n - A047160(n) = A112823(n) (for n >= 3). - Jason Kimberley, Aug 31 2011

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Sep 21 2000