A335250 Numbers m such that twice the number of unordered Goldbach partitions of 2m equals the number of unordered Goldbach partitions of 4m.

1, 4, 9, 15, 21, 30, 40, 46, 69, 70, 79, 81, 82, 106, 114, 199, 229, 256, 361, 391, 469, 586, 754, 760, 766, 826, 892, 1471, 1483, 1525, 1591, 1609, 1624, 1816, 2194, 2206, 2454, 2629, 2869, 3955, 3961, 3964, 6406, 6946, 11749

Offset

1,2

Comments

Integers m such that 2*A002375(2m) = A002375(4m).

It is conjectured that the last term in this sequence is a(45)=11749.

Links

Table of n, a(n) for n=1..45.

Index entries for sequences related to Goldbach conjecture

Example

m=4 is a term because 2m=8 has the partition (3,5) while 4m=16 has the partitions (3,13) and (5,11).

Prog

(PARI) for(n=1, 200000, x=0; y=0; forprime(i=2, 2*n-1, if(i<=n && isprime(2*n-i), x=x+1; ); if(isprime(4*n-i), y=y+1; ); ); if(2*x==y, print1(n, ", ")))

Crossrefs

Cf. A002375, A335226.

Sequence in context: A358243 A099055 A162801 * A103396 A103400 A103399

Adjacent sequences: A335247 A335248 A335249 * A335251 A335252 A335253

Keyword

nonn,more

Author

Craig J. Beisel, May 28 2020

Status

approved