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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
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: A136254 A146528 A345016 * A176777 A318761 A020153
KEYWORD
nonn
AUTHOR
J. Stauduhar, Sep 16 2012
STATUS
approved

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Last modified April 17 04:44 EDT 2024. Contains 371756 sequences. (Running on oeis4.)