User blog comment:Primussupremus/Extended busy beaver or super sigma./@comment-80.98.179.160-20180123181310

Let BBB0(n)=BBnn(n), and BBBx(n)=BBBx-1n(n). Define BBBB, BBBBB, BBBBBB,... in similar manner, except diagonalizing over BBB, BBBB, BBBBB,... Define: Continue with BB(999)(9999). That's way larger.
 * B(n,k,m)=BBBBB...(m Bs)...BBBBk(n)
 * B(n,k)=B(n,k,k)
 * B(n)=B(n,n,n).