cp's OEIS Frontend

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

%I A254713 #17 Feb 16 2025 08:33:24
%S A254713 4,5,6,7,11,13,17,19,23,29,31,53,59,61,67,73,83,89,97,101,103,109,113,
%T A254713 127,131,139,151,157,163,173,179,191,193,199,223,227,229,251,263,271,
%U A254713 307,313,337,347,353,359,367,379,389,401,449,479,521,523,577,587,599,601,607,613,631,643
%N A254713 All numbers k such that the number of distinct parts of all A045917(k) Goldbach partitions of 2k is prime.
%C A254713 Conjecture: a(k) is prime for k > 3. Tested for k up to 3*10^4.
%H A254713 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html ">Goldbach Partition</a>.
%e A254713 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.
%e A254713 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
%t A254713 lstIn={};lstFin={};
%t A254713 goldPart[x_]:=Module[{h=x/2},While[h>1,If[And[PrimeQ[h],PrimeQ[x-h]],AppendTo[lstIn,{h,x-h}]];h--];
%t A254713 lstFin=Length[Union[Flatten[lstIn]]];lstIn={};lstFin];
%t A254713 a254713=Flatten[Position[PrimeQ[goldPart/@Range[2,2002,2]],True]]
%Y A254713 Cf. A035026, A002372, A045917.
%K A254713 easy,nonn
%O A254713 1,1
%A A254713 _Ivan N. Ianakiev_, Feb 06 2015
%E A254713 Edited. _Wolfdieter Lang_, Feb 23 2015