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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.
1
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.
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
KEYWORD
nonn
AUTHOR
Craig J. Beisel, May 27 2020
STATUS
approved