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 A216051 Even numbers m that have an odd number of Goldbach partitions whose lesser and greater elements each sum to a prime. 1
 4, 6, 8, 12, 22, 30, 40, 44, 48, 54, 78, 136, 156, 158, 170, 178, 206, 236, 288, 298, 380, 394, 500, 594, 624, 648, 650, 750, 810, 952, 1062, 1070, 1162, 1280, 1500, 1616, 1680, 1742, 1764, 2104, 2120, 2268, 2332, 2470, 2494, 2500, 2600, 2992, 3094, 3134 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS J. Stauduhar, Table of n, a(n) for n = 1..380 EXAMPLE 4, 6, 8, and 12 have just one Goldbach partition each, so the sum of the lesser and greater elements of each partition is prime, giving the first four terms in the sequence. Three Goldbach partitions comprise 22:  (3,19), (5,17) and (11,11).  3 + 5 + 11 = 19, and 11 + 17 + 19 = 47. Both 19 and 47 are prime, so a(5) = 22. MATHEMATICA f[n_] := Module[{lst={}}, For[i=2, i<=n, i+=2, parts=Select[ IntegerPartitions[i, {2}], And@@PrimeQ /@#&]; If[And@@PrimeQ[Plus@@parts[[Range[1, Length[parts]], {1, 2}]]],     AppendTo[lst, i]]; ]; lst]; f[1000](* J. Stuaduhar, Sep 18 2012 *) CROSSREFS Sequence in context: A323059 A136254 A146528 * A176777 A318761 A020153 Adjacent sequences:  A216048 A216049 A216050 * A216052 A216053 A216054 KEYWORD nonn AUTHOR J. Stauduhar, Sep 16 2012 STATUS approved

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Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)