A375886 Numbers k such that 2k and 4k have the same number of Goldbach partitions into primes.

2, 3, 5, 7, 8, 11, 13, 23, 37, 41, 47, 53, 56, 71, 77, 83, 92, 122, 137, 158, 167, 248

Offset

1,1

Comments

No further terms up to 10^5.

Links

Table of n, a(n) for n=1..22.

Example

Both 10 = 3+7 = 5+5 and 20 = 3+17 = 7+13 have two Goldbach partitions, so 5 is a term.

Maple

N:= 100000: # to test k <= N
P:= select(isprime, [2, seq(i, i=3..4*N-2, 2)]):
G:= Vector(4*N):
for i from 1 to nops(P) do
   jmax:= ListTools:-BinaryPlace(P, 4*N-P[i]);
   if jmax < i then break fi;
   J:=  P[i..jmax]+~ P[i];
   G[J]:= G[J] +~ 1
od:
select(t -> G[2*t] = G[4*t], [$1..N]); # Robert Israel, Sep 02 2024

Mathematica

f[n_]:=Length[Select[2*n-Prime[Range[PrimePi[n]]], PrimeQ]];
Select[Range[250], f[#]==f[2*#]&]

Crossrefs

Cf. A045917.

Sequence in context: A375270 A186285 A378170 * A190855 A190810 A278591

Adjacent sequences: A375883 A375884 A375885 * A375887 A375888 A375889

Keyword

nonn,more

Author

Ivan N. Ianakiev, Sep 01 2024

Status

approved