https://oeis.org/draft/A158709
 

[QUOTE]Apart from the first term, primes such that a Goldbach partition with a pair of them, will lead to a Goldbach partition for the next even number in their sums Collatz chain.[/QUOTE] I was told to blog this in PM. Examples:

6=3+3 ->10=5+5; 10=3+7->16=5+11 did have a rough 21 digit example, but may have to find it again.

[QUOTE] Example: 100000000000000008947+ 100000000000000008899 =200000000000000017846
->150000000000000013349+150000000000000013421 =300000000000000026770[/QUOTE]

[CODE]my(a=0,b=[]);for(x=1,n,if((a-x)>0&&setminus(b,[a-x])==[],b=concat(b,[a-x]);a-=x;print(a),if(setminus(b,[a+x])==[],b=concat(b,[a+x]);a+=x;print(a),print("fails at x="x);break())))[/CODE]

Fails at x=26 apparently.

Yes I'm weird
 

[CODE]my(s=self());return(select(r->r=="e",Vec(Str(s))))[/CODE]

A code that searches itself.