A216047 Consider the ordered Goldbach partitions of the even numbers m. Then a(n) is the least m which contains prime(n) such partitions composed of odd primes.

8, 10, 22, 34, 106, 178, 202, 358, 386, 502, 802, 694, 1322, 958, 1198, 1366, 1546, 1654, 2066, 2578, 2402, 2446, 2722, 2894, 2974, 3866, 3646, 3986, 4054, 4162, 4954, 5714, 5182, 6082, 6334, 6598, 6614, 6742, 7402, 8158, 7846, 8782, 8566, 9274, 9382, 9502

Offset

1,1

Comments

A002372(a(n)/2) = p.

Links

J. Stauduhar and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 100 terms from J. Stauduhar)

Example

With n = 1:  prime(1) = 2, so we want the least m that has 2 such partitions.  For m = 4, 4 = {2+2}, but 2 is not an odd prime number.  For m = 6, 6 has one such partition, {3+3}, but 1 is not a prime number.  For m = 8, 8 has two such partitions, {3+5, 5+3}, so a(1) = 8.
a(3) = 22: With n = 3, prime(3) = 5 and 22 = {3+19, 5+17, 11+11, 17+5, 19+3}.

Mathematica

nn = 10^4; ps = Boole[PrimeQ[Range[1, 2*nn, 2]]]; lst = Table[Sum[ps[[i]] ps[[n - i + 1]], {i, n}], {n, nn}]; t = {}; p = 0; While[p = NextPrime[p]; pos = Position[lst, p, 1, 1]; pos != {}, AppendTo[t, 2*pos[[1, 1]]]]; t (* T. D. Noe, Aug 31 2012 *)

Crossrefs

Cf. A002372.

Sequence in context: A338820 A302429 A292999 * A032488 A102844 A303199

Adjacent sequences: A216044 A216045 A216046 * A216048 A216049 A216050

Keyword

nonn

Author

J. Stauduhar, Aug 30 2012

Status

approved