A216048 Consider the unordered Goldbach partitions of the even numbers m. Then a(n) is the least m which contains prime(n) such partitions composed of odd primes.

10, 22, 48, 78, 144, 168, 288, 210, 474, 480, 570, 714, 630, 930, 924, 1302, 1386, 1380, 1500, 1590, 1470, 2160, 1680, 2838, 2100, 2772, 3498, 2640, 2760, 3060, 4452, 4284, 4170, 4110, 3780, 4650, 5874, 3990, 4950, 5550, 8802, 8706, 5850, 6480, 7728, 7812

Offset

1,1

Comments

A002375(a(n)/2) = p.

Links

J. Stauduhar, Table of n, a(n) for n = 1..100

Example

With n = 1:  prime(1) = 2, so we want the least m that has 2 such partitions.  For m = 6, 6 has one such partition, {3+3}, but 1 is not a prime number.  For m = 8, 8 has one such partition, {3+5}, but 1 is not a prime number.  For m = 10, 10 has two such partitions, {3+7, 5+5}, so a(1) = 10.
a(3) = 48: With n = 3, prime(3) = 5 and 48 = {5+43, 7+41, 11+37, 17+31, 19+29}.

Mathematica

nn = 10^4; ps = Boole[PrimeQ[Range[1, 2*nn, 2]]]; lst =
Table[Sum[ps[[i]] ps[[n - i + 1]], {i, Ceiling[n/2]}], {n,
   nn}]; t = {}; p = 0; While[p = NextPrime[p];
pos = Position[lst, p, 1, 1]; pos != {}, AppendTo[t, 2*pos[[1, 1]]]];
t (* Modified T. D. Noe's code from A216047 *) (* J. Stauduhar, Sep 01 2012 *)

Crossrefs

Cf. A002375.

Sequence in context: A242234 A104867 A179877 * A079861 A014008 A219744

Adjacent sequences: A216045 A216046 A216047 * A216049 A216050 A216051

Keyword

nonn

Author

J. Stauduhar, Aug 31 2012

Status

approved