%I #25 Jun 08 2020 17:33:52
%S 6,16,19,28,34,49,61,64,76,91,94,124,133,154,163,166,184,208,214,244,
%T 250,259,271,277,286,301,316,334,346,355,364,403,430,439,451,481,496,
%U 511,556,619,649,679,706,709,724,799,802,859,874,979,982,994,1006,1024,1069,1099
%N Numbers m such that twice the number of unordered Goldbach partitions of 2m is less than the number of unordered Goldbach partitions of 4m.
%C Integers m such that 2*A002375(2m) < A002375(4m).
%C It is conjectured that the last term in this sequence is a(114)=22564.
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%e 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).
%o (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, ", ")))
%Y Cf. A002375, A335250, shares a number of terms with A137820.
%K nonn
%O 1,1
%A _Craig J. Beisel_, May 27 2020