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%I #19 Jun 18 2016 00:47:28
%S 6,8,12,28,40,52,56,68,124,128,136,172,176,188,226,262,266,304,308,
%T 394,396,398,412,416,442,446,484,488,544,548,556,560,608,634,638,668,
%U 682,686,694,696,698,724,728,736,740,754,758,772,776,802,806,874,878,934
%N Even numbers with a unique resolution as the sum of two primes, each of which has a twin.
%C The sequence is infinite only if the number of twin primes is infinite.
%C Note that not all even integers can be written as the sum of two twins (e.g. 94, 96, 98,...).
%e 6 = 3 + 3 is an element since (3,5) are twins, as is 8 = 5 + 3.
%e 10 = 7 + 3 = 5 + 5 is not an element, since it is not uniquely resolved, even though the two resolutions both involve primes with twins.
%t ok[n_] := 1 == Length@ IntegerPartitions[n, {2}, Select[Prime@ Range@ PrimePi@ n, Or @@ PrimeQ[# + {-2, 2}] &]]; Select[2 Range[500], ok] (* _Giovanni Resta_, Jun 06 2016 *)
%Y Cf. A129363, A007534.
%K nonn
%O 1,1
%A _Thomas Curtright_, Jun 06 2016
%E a(7)-a(54) from _Giovanni Resta_, Jun 06 2016
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