已知:
G(1)=3↑↑↑↑3
G(2)=3↑...↑3(G(1)个3)
......
那么
G(1,0)=G(G(...(G(64)...)(省略G(64)对G())
G(1,1)=G(G(...(G(1,0)...)(省略G(1,0)对G())
......
G(1,n)=G(G(...(G(1,n-1)...)(省略G(1,n-1)对G())
G(2,0)=G(1,G(1,G(...)))(省略G(1,G(1,0))对G(1,))
...
G(n,0)=G(n-1,G(n-1,G(...G(n-1,0)...)))(省略G(n-1,G(n-1,0))对G(n-1,))
G(n,m)=G(n-1,G(n-1,G(...G(n,m-1)...)))(省略G(n,m-1)对G(n-1,))
一阶段截止
对于超过两位的G,进行如下操作
G(a,x1,x2,...,xn)(显然n+1位)
(非特殊说明的话只要写的是英文字母就不是0)
规则1:
G(0,x1,x2,...,xn)(n+1位)=G(G(G(x1,x2,x3,...,xn)(n位),x2,x3,...,xn)(n位),G(G(x1,x2,x3,...,xn)(n位),x2,x3,...,xn)(n位),G(G(x1,x2,x3,...,xn)(n位),x2,x3,...,xn)(n位),...,G(G(x1,x2,x3,...,xn)(n位),x2,x3,...,xn)(n位))(n位)
规则2:
G(a,0,0,...,0)(n+1位)=G(a-1,G(a-1,0,0,...,0)(n+1位),G(a-1,0,0,...,0)(n+1位),...,G(a-1,0,0,...,0)(n+1位))(n+1位)
规则3:
G(a,x1,x2,...,xn)(n+1位)=G(a-1,G(a,x1,x2,...,x(n-1),(xn-1))(n+1位),G(a,x1,x2,...,x(n-1),(xn-1))(n+1位),......,G(a,x1,x2,...,x(n-1),(xn-1))(n+1位))(n+1位)
规则4:
G(a,...x(n-m+1)=0...,x(n-1)=0,xn=0)(最后m位为0)=G(a,...,x(n-m-1),(x(n-m)-1),x(n-m+1)=G(a-1,x1,x2,...,x(n-m),x(n-m+1),...,xn)(n+1位),x(n-m+2)=G(a-1,x1,x2,...,x(n-m),x(n-m+1),...,xn)(n+1位),...,xn=G(a-1,x1,x2,...,x(n-m),x(n-m+1),...,xn)(n+1位))
G(0,,n)=G(G(n),G(n),...,G(n))(G(n)个G(n))
G(a,,0)=G((a-1),,G((a-1),,1))
G(a,,b)=G(G(a,,(b-1)),G(a,,(b-1)),...,G(a,,(b-1)))(G(a,,(b-1))位)(G(a,,(b-1))个G(a,,(b-1)))
对于超过两位的G,进行如下操作
G(a,,x1,,x2,,...,,xn)(显然n+1位)
(非特殊说明的话只要写的是英文字母就不是0)
规则1:
G(0,,x1,,x2,,...,,xn)(n+1位)=G(G(G(x1,,x2,,x3,,...,,xn)(n位),,x2,,x3,,...,,xn)(n位),,G(G(x1,,x2,,x3,,...,,xn)(n位),,x2,,x3,,...,,xn)(n位),,G(G(x1,,x2,,x3,,...,,xn)(n位),,x2,,x3,,...,,xn)(n位),,...,,G(G(x1,,x2,,x3,,...,,xn)(n位),,x2,,x3,,...,,xn)(n位))(n位)
规则2:
G(a,,0,,0,,...,,0)(n+1位)=G(a-1,,G(a-1,,0,,0,,...,,0)(n+1位),,G(a-1,,0,,0,,...,,0)(n+1位),,...,,G(a-1,,0,,0,,...,,0)(n+1位))(n+1位)
规则3:
G(a,,x1,,x2,,...,,xn)(n+1位)=G(a-1,,G(a,,x1,,x2,,...,,x(n-1),,(xn-1))(n+1位),,G(a,,x1,,x2,,...,,x(n-1),,(xn-1))(n+1位),,......,,G(a,,x1,,x2,,...,,x(n-1),,(xn-1))(n+1位))(n+1位)
规则4:
G(a,,...x(n-m+1)=0...,,x(n-1)=0,,xn=0)(最后m位为0)=G(a,,...,,x(n-m-1),,(x(n-m)-1),,x(n-m+1)=G(a-1,,x1,,x2,,...,,x(n-m),,x(n-m+1),,...,,xn)(n+1位),,x(n-m+2)=G(a-1,,x1,,x2,,...,,x(n-m),,x(n-m+1),,...,,xn)(n+1位),,...,,xn=G(a-1,,x1,,x2,,...,,x(n-m),,x(n-m+1),,...,,xn)(n+1位))
以此类推......
G((1))=G(1,,...,1)(G(1,1)个,)
G((2))=G(G((1)),,...,G((1)))(G((1))个,)
......
二阶段截止
求算:
{
G(n,n)增长率?
G(n,,n)增长率?
G((n))增长率?
}