A002373 Smallest prime in decomposition of 2n into sum of two odd primes. (Formerly M2273 N0899)

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

3,1

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

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 *)

Prog

(Haskell) a002373 n = head $ dropWhile ((== 0) . a010051 . (2*n -)) a065091_list -- Reinhard Zumkeller, Feb 29 2012
(PARI) a(n)=forprime(p=3, n, if(isprime(2*n-p), return(p))) \\ Charles R Greathouse IV, May 18 2015

Crossrefs

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

Sequence in context: A301738 A302387 A049613 * A236569 A103153 A162022

Adjacent sequences: A002370 A002371 A002372 * A002374 A002375 A002376

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from Ray Chandler, Sep 19 2003

Status

approved