A335226 Numbers m such that twice the number of unordered Goldbach partitions of 2m is less than the number of unordered Goldbach partitions of 4m.

6, 16, 19, 28, 34, 49, 61, 64, 76, 91, 94, 124, 133, 154, 163, 166, 184, 208, 214, 244, 250, 259, 271, 277, 286, 301, 316, 334, 346, 355, 364, 403, 430, 439, 451, 481, 496, 511, 556, 619, 649, 679, 706, 709, 724, 799, 802, 859, 874, 979, 982, 994, 1006, 1024, 1069, 1099

Offset

1,1

Comments

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

It is conjectured that the last term in this sequence is a(114)=22564.

Links

Table of n, a(n) for n=1..56.

Index entries for sequences related to Goldbach conjecture

Example

m=6 is a term because 2m=12 has the partition (5,7) while 4m=24 has the partitions (5,19),(7,17) and (11,13).

Prog

(PARI) for(n=1, 100000, 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, A335250, shares a number of terms with A137820.

Sequence in context: A217186 A101239 A242331 * A104392 A291746 A037001

Adjacent sequences: A335223 A335224 A335225 * A335227 A335228 A335229

Keyword

nonn

Author

Craig J. Beisel, May 27 2020

Status

approved