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

Author

Craig J. Beisel, May 28 2020

Keywords

• nonn
• more

Comments

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

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

Examples

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

Links

• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A002375, A335226.

Programs

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, ", ")))