A002373 Smallest prime in decomposition of 2n into sum of two odd primes.

3, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 7, 3, 3, 5, 7, 3, 5, 3, 3, 5, 3, 5, 7, 3, 5, 7, 3, 3, 5, 7, 3, 5, 3, 3, 5, 7, 3, 5, 3, 5, 7, 3, 5, 7, 19, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 7, 13, 11, 13, 19, 3, 5, 3, 5, 7, 3, 3, 5, 7, 11, 11, 3, 3, 5, 7, 3, 5, 7, 3, 5, 3, 5, 7, 3, 5, 7, 3, 3, 5, 7, 11, 11, 3, 3, 5, 3

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

Comments

See A020481 for another version.

a(A208662(n)) = A065091(n) and a(m) <> A065091(n) for m < A208662(n). - Reinhard Zumkeller, Feb 29 2012

Records are in A025019, their indices in A051610. - Ralf Stephan, Dec 29 2013

Note that these primes do not all belong to a twin prime pair. The first instance is a(110) = 23. - Michel Marcus, Aug 17 2020 from a suggestion by Pierre CAMI

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
• Eric Weisstein's World of Mathematics, Goldbach Partition
• Wikipedia, Goldbach's conjecture
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A002372, A002374, A014092, A065091, A010051.

Programs

Haskell

a002373 n = head $ dropWhile ((== 0) . a010051 . (2*n -)) a065091_list -- Reinhard Zumkeller, Feb 29 2012

Mathematica

Table[k = 2; While[q = Prime[k]; ! PrimeQ[2*n - q], k++]; q, {n, 3, 100}] (* Jean-François Alcover, Apr 26 2011 *)
Table[Min[Flatten[Select[IntegerPartitions[2*n,{2}],AllTrue[ #,OddQ] && AllTrue[#,PrimeQ]&]]],{n,3,100}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 31 2020 *)

PARI

a(n)=forprime(p=3,n,if(isprime(2*n-p), return(p))) \\ Charles R Greathouse IV, May 18 2015

Extensions

More terms from Ray Chandler, Sep 19 2003