User:Kyodaisuu/Bashicu

As is now trying to extend his pair sequence system to matrix, and he is posting his result in his Japanese blog, here I paste some of his result.

Trio sequence
Here (s)he wrote a verification code of tentative algorithm of trio sequence. It runs on yabasic.

dim A(1000):dim B(1000):dim C(1000):D=1 A(0)=0:A(1)=1:A(2)=1:A(3)=2:A(4)=2 B(0)=0:B(1)=1:B(2)=1:B(3)=2:B(4)=2 C(0)=0:C(1)=1:C(2)=0:C(3)=1:C(4)=0 F=4 while (F>=0) for I=0 to F    print "(",A(I),",",B(I),",",C(I),")"; next I  print "[",D,"]" if B(F)=0 then G=1 else G=0 endif if C(F)=0 then H=1 else H=0 endif for I=0 to F*G if A(F-I)200 break wend

Output of this program

(0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)[1] (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,2,1)[1] (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,2,0)[1] (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,1,0)[1] (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,0,0)(4,1,1)(4,1,0)(5,2,1)(5,1,0)[1] (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,0,0)(4,1,1)(4,1,0)(5,2,1)(5,0,0)(6,1,1)(6,1,0)(7,2,1)[1] (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,0,0)(4,1,1)(4,1,0)(5,2,1)(5,0,0)(6,1,1)(6,1,0)(7,2,0)[1] (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,0,0)(4,1,1)(4,1,0)(5,2,1)(5,0,0)(6,1,1)(6,1,0)(7,1,0)[1] (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,0,0)(4,1,1)(4,1,0)(5,2,1)(5,0,0)(6,1,1)(6,1,0)(7,0,0)(8,1,1)(8,1,0)[1] (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,0,0)(4,1,1)(4,1,0)(5,2,1)(5,0,0)(6,1,1)(6,1,0)(7,0,0)(8,1,1)(8,0,0)(9,1,1)[1] (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,0,0)(4,1,1)(4,1,0)(5,2,1)(5,0,0)(6,1,1)(6,1,0)(7,0,0)(8,1,1)(8,0,0)(9,1,0)[1]

Calculation

\begin{eqnarray*} (0,0,0)(1,1,1)&=&θ(Ω_ω) \\ (0,0,0)(1,1,1)(1,0,0)&=&θ(Ω_ω)・ω \\ (0,0,0)(1,1,1)(1,0,0)(2,1,1)&=&θ(Ω_ω)^2 \\ (0,0,0)(1,1,1)(1,0,0)(2,1,1)(2,0,0)(3,1,1)&=&θ(Ω_ω)^{θ(Ω_ω)} \\ (0,0,0)(1,1,1)(1,1,0)&=&ε_{θ(Ω_ω)+1} = ψ(ψ(Ω_ω)+1) \\ (0,0,0)(1,1,1)(1,1,0)(2,0,0)(3,1,1)&=&ψ(ψ(Ω_ω)+ψ(Ω_ω)) \\ (0,0,0)(1,1,1)(1,1,0)(2,0,0)(3,1,1)(3,1,0)&=&ψ(ψ(ψ(Ω_ω+1))) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,0)&=&ψ(ψ_1(Ω_ω)+1) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,0)(3,3,0)&=&ψ(ψ_1(ψ_2(Ω_ω)+1)) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,0)(3,3,0)&=&ψ(ψ_1(ψ_2(ψ_3(Ω_ω)+1))) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)&=&ψ(Ω_ω+1) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(1,1,0)(2,1,1)&=&ψ(Ω_ω+2) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,0,0)&=&ψ(Ω_ω+ω) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)&=&ψ(Ω_ω+Ω) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,2,0)&=&ψ(Ω_ω+ψ_1(0)) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,2,0)(4,3,0)&=&ψ(Ω_ω+ψ_1(ψ_2(0))) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,2,1)&=&ψ(Ω_ω+Ω_ω) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,2,1)(3,1,0)&=&ψ(Ω_ω・ω) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,2,1)(3,1,0)(4,2,1)&=&ψ(Ω_ω^2) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,2,1)(3,1,0)(4,2,1)\\ (4,1,0)(5,2,1)&=&ψ(Ω_ω^{Ω_ω}) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,2,1)(3,1,0)(4,2,1)\\ (4,1,0)(5,2,1)(5,1,0)(6,2,1)&=&ψ(Ω_ω^{Ω_ω^2}) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,1,0)(3,2,1)(3,1,0)(4,2,1) \\ (4,1,0)(5,2,1)(5,1,0)(6,2,1)(6,1,0)(7,2,1)&=&ψ(Ω_ω^{Ω_ω^{Ω_ω}})) \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)&=&ψ(ψ_ω(0))=ψ(ε_{Ω_ω+1})=θ(ε_{Ω_ω+1}) \\ \end{eqnarray*}