A254713 All numbers k such that the number of distinct parts of all A045917(k) Goldbach partitions of 2k is prime.

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

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