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%I #22 Sep 04 2012 19:21:52
%S 8,10,22,34,106,178,202,358,386,502,802,694,1322,958,1198,1366,1546,
%T 1654,2066,2578,2402,2446,2722,2894,2974,3866,3646,3986,4054,4162,
%U 4954,5714,5182,6082,6334,6598,6614,6742,7402,8158,7846,8782,8566,9274,9382,9502
%N 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.
%C A002372(a(n)/2) = p.
%H J. Stauduhar and Donovan Johnson, <a href="/A216047/b216047.txt">Table of n, a(n) for n = 1..1000</a> (first 100 terms from J. Stauduhar)
%e 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.
%e a(3) = 22: With n = 3, prime(3) = 5 and 22 = {3+19, 5+17, 11+11, 17+5, 19+3}.
%t 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 *)
%Y Cf. A002372.
%K nonn
%O 1,1
%A _J. Stauduhar_, Aug 30 2012
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