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%I #22 Jan 15 2023 00:27:35
%S 6,10,22,34,48,60,78,84,90,114,120,168,180,210,300,330,390,420,510,
%T 630,780,840,990,1050,1140,1260,1470,1650,1680,1890,2100,2310,2730,
%U 3150,3570,3990,4200,4410,4620,5250,5460,6090,6510,6930,7980,8190,9030,9240
%N Numbers that can be expressed as the sum of two odd primes in more ways than any smaller even number.
%C The terms up to 114 are identical with A001172. The record-setting number of decompositions is given by A082918.
%C It appears that every primorial number (A002110) greater than 30 is in this sequence. Sequence A116979 gives the number of decompositions for n equal to a primorial number. - _T. D. Noe_, Mar 15 2010
%H Bill Hannaford, <a href="/A082917/b082917.txt">Table of n, a(n) for n = 1..420</a> (first 244 terms from T. D. Noe)
%e a(1) = 6 = 3 + 3.
%e a(2) = 10 because 10 is the smallest number that can be written in two ways: 10 = 3 + 7 = 5 + 5.
%t kmax = 40000;
%t ip[k_] := IntegerPartitions[k, {2}, Select[Range[3, k-1], PrimeQ]];
%t seq = Module[{k, lg, record = 0, n = 0}, Reap[For[k = 6, k <= kmax, k = k+2, lg = Length[ip[k]]; If[lg > record, record = lg; n = n+1; Print["a(", n, ") = ", k]; Sow[k]]]][[2, 1]]] (* _Jean-François Alcover_, Jun 04 2022 *)
%Y Cf. A002375, A001172, A082918. A109679 is another version of the same sequence.
%K nonn
%O 1,1
%A _Hugo Pfoertner_, Apr 15 2003
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