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 A274001 Even numbers with a unique resolution as the sum of two primes, each of which has a twin. 0
 6, 8, 12, 28, 40, 52, 56, 68, 124, 128, 136, 172, 176, 188, 226, 262, 266, 304, 308, 394, 396, 398, 412, 416, 442, 446, 484, 488, 544, 548, 556, 560, 608, 634, 638, 668, 682, 686, 694, 696, 698, 724, 728, 736, 740, 754, 758, 772, 776, 802, 806, 874, 878, 934 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence is infinite only if the number of twin primes is infinite. Note that not all even integers can be written as the sum of two twins (e.g. 94, 96, 98,...). LINKS EXAMPLE 6 = 3 + 3 is an element since (3,5) are twins, as is 8 = 5 + 3. 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. MATHEMATICA 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 *) CROSSREFS Cf. A129363, A007534. Sequence in context: A072057 A212351 A327240 * A324212 A160133 A057710 Adjacent sequences:  A273998 A273999 A274000 * A274002 A274003 A274004 KEYWORD nonn AUTHOR Thomas Curtright, Jun 06 2016 EXTENSIONS a(7)-a(54) from Giovanni Resta, Jun 06 2016 STATUS approved

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Last modified June 21 00:55 EDT 2021. Contains 345329 sequences. (Running on oeis4.)