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 A254713 All numbers k such that the number of distinct parts of all A045917(k) Goldbach partitions of 2k is prime. 1
 4, 5, 6, 7, 11, 13, 17, 19, 23, 29, 31, 53, 59, 61, 67, 73, 83, 89, 97, 101, 103, 109, 113, 127, 131, 139, 151, 157, 163, 173, 179, 191, 193, 199, 223, 227, 229, 251, 263, 271, 307, 313, 337, 347, 353, 359, 367, 379, 389, 401, 449, 479, 521, 523, 577, 587, 599, 601, 607, 613, 631, 643 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: a(k) is prime for k > 3. Tested for k up to 3*10^4. LINKS Table of n, a(n) for n=1..62. Eric Weisstein's World of Mathematics, Goldbach Partition. EXAMPLE For k = 4, 2k = 8. The number of the distinct Goldbach parts of 8 (3 and 5) is prime, therefore 4 is in the sequence. 5 is in the sequence because the 2 = A045917(5) Goldbach partitions of 10 are 5 + 5 and 3 + 7, and there are 3 distinct parts, namely 3, 5 and 7. - Wolfdieter Lang, Feb 23 2015 MATHEMATICA lstIn={}; lstFin={}; goldPart[x_]:=Module[{h=x/2}, While[h>1, If[And[PrimeQ[h], PrimeQ[x-h]], AppendTo[lstIn, {h, x-h}]]; h--]; lstFin=Length[Union[Flatten[lstIn]]]; lstIn={}; lstFin]; a254713=Flatten[Position[PrimeQ[goldPart/@Range[2, 2002, 2]], True]] CROSSREFS Cf. A035026, A002372, A045917. Sequence in context: A191164 A363089 A004714 * A014098 A086101 A131260 Adjacent sequences: A254710 A254711 A254712 * A254714 A254715 A254716 KEYWORD easy,nonn AUTHOR Ivan N. Ianakiev, Feb 06 2015 EXTENSIONS Edited. Wolfdieter Lang, Feb 23 2015 STATUS approved

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Last modified April 20 17:12 EDT 2024. Contains 371845 sequences. (Running on oeis4.)