巨大数列数(Huge sequence number)
A=9:dim B[∞] for C=0 to 9 for D=0 to A B[D]=D next for E=A to 0 step -1 A=A+1 for F=0 to E if B[E-F]<B[E] then for G=1 to A B[E+G-1]=B[E-F] next E=E+A:F=E endif next next next print A 例 0,1,2,3,2 0,1,2,3,2,1,1 0,1,2,3,2,1,0,0
Hu(x)=ω.
超巨大数列数(Hyper huge sequence number)
A=9:dim B[∞] for C=0 to 9 for D=0 to A B[D]=D next for E=A to 0 step -1 A=A+1 for F=0 to E if B[E-F]<B[E]-G | B[E-F]=0 then if F=B[E]-B[E-F] & 0<B[E-F] then G=B[E]-B[E-F] else if 0<G & 0<B[E-F] then F=G:G=G-1 for H=1 to A*F if 0<G then I=B[E-F]+G else I=B[E-F-H+1] B[E]=I:E=E+1 next F=E:G=0 endif endif next next next print A
原始数列数(Primitive sequence number)
A=9:dim B[∞] for C=0 to 9 for D=0 to A B[D]=D next for E=A to 0 step -1 A=A*A for F=0 to E if B[E-F]<B[E] or B[E]=0 then G=F:F=E next for H=1 to A*G B[E]=B[E-G]:E=E+1 next next next print A 例 0,1,2,2 0,1,2,1,2 0,1,2,1,1 0,1,2,1,0,1,2,1
または、一次数列数
P(x)=ε_0
階差数列数(Difference sequence number)
A=9:dim B[∞] for C=0 to 9 for D=0 to A B[D]=D next for E=A to 0 step -1 A=A*A for F=0 to E if B[E-F]<B[E] | B[E]=0 then G=F:F=E if 0<B[E-G] then for H=1 to B[E-G] if B[E-G-1]=B[E-G]-1 then G=G+1:I=I+1 else H=B[E-G+H] next endif endif next for J=1 to A*G B[E]=B[E-G]+I:E=E+1 next I=0 next next pritn A
108Hassiumさんの大偽原始数列を参考にする。L(x)=φ_ω(0)
超数列数(Hyper sequence number)
A=9:dim B[∞] for C=0 to 9 for D=1 to A B[D]=D next for E=A to 0 step -1 A=A*A for F=0 to E if B[E-F]<B[E] then if G=0 then H=F for I=0 to H if B[E-F+I]<B[E-H+I] then F=E:I=H:J=1 if B[E-H+I]<B[E-F+I] then I=H next if J=0 then G=F else J=0 endif next for K=1 to A*G B[E]=B[E-G]:E=E+1 next G=0 next next print A 例 0,1,2,3,2,3 0,1,2,3,2,2,3,2 0,1,2,3,2,2,3,1,2,3,2,2,3 0,1,2,3,2,2,3,1,2,3,2,2,2,2 0,1,2,3,2,2,3,1,2,3,2,2,2,1,2,3,2,2,3,1,2,3,2,2,2,1,2,3,2,2,3,1,2,3,2,2,2
H(x)=Γ_0
ペア数列数(Pair sequence number)
dim A[∞],B[∞]:C=9 for D=0 to 9 for E=0 to C A[E]=E:B[E]=E next for F=C to 0 step -1 C=C*C for G=0 to F if A[F]=0 | A[F-G]<A[F]-H then if B[F]=0 then I=G:G=F else H=A[F]-A[F-G] if B[F-G]<B[F] then I=G:G=F endif endif next for J=1 to C*I A[F]=A[F-I]+H:B[F]=B[F-I]:F=F+1 next H=0 next next print C 例 (0,0)(1,1)(2,1)(3,1)(2,0)(1,1)(2,1)(3,1) (0,0)(1,1)(2,1)(3,1)(1,0)(1,1)(2,1)(3,0)(4,1)(5,1)(6,1)(5,0)(4,1)(5,1)
または、二次数列数 Pair(x)=Ψ_Ω(Ω_ω)
悪い部分決定に端の行の下降無しで(0,0)(1,1)(2,1)(3,1)(1,0)(1,1)(2,1)(3,1)=Γ_{ω+1}が停止しな い最小の行列である。バシクトリ=(0,0)(1,1)(2,1)(3,1)(2,0)(1,1)(2,1)(3,1)[3]
バシク小行列数(Bashicu little matrix number)
A=9:dim B[∞,∞],C[∞,∞],D[∞] for E=0 to 9 for F=1 to A B[2,F]=1:C[1,F]=1 next for G=2 to 1 step -1 A=A*A for H=0 to G for I=1 to F if B[G-H,I]<B[G,I]-D[I] | B[G,1]=0 then if 0<B[G,I+1] | 1<I & 0<B[G-H,I+1] then D[I]=B[G,I]-B[G-H,I] else J=H:H=G-1:I=F endif else I=F endif next next for K=1 to J for L=1 to F C[K+1,L]=0 next for M=G-J+K to G-J step -1 if B[M,1]<B[G-J+K,1] then for N=1 to F if B[M,N]<B[G-J+K,N] & C[M,N]=1 then C[K+1,N]=1 next M=G-J endif next next for O=1 to F D[O]=0 if 0<B[G,O+1] then D[O]=B[G,O]-B[G-J,O] next for P=1 to A for Q=1 to J for R=1 to F if C[Q,R]=1 then B[G,R]=B[G-J,R]+D[R] else B[G,R]=B[G-J,R] next G=G+1 next next for S=1 to F D[S]=0 next next next print A
ベースはBM3。BLIM=BM(0,0,0)(1,1,1)(2,2,2)?
急数列数(Sudden sequence number)
A=9:dim B[∞] for C=0 to 9 for D=1 to A B[D+1]=D next for E=A+1 to 1 step -1 A=A*A for F=0 to E-1 if B[E-F]<B[E]-G then if H=0 then I=F if G+1<B[E]-B[E-F] then G=G+1 for J=0 to I if B[E-F+J]<B[E-I+J]-G then F=E-1:J=I:K=1 if B[E-I+J]-G<B[E-F+J] then J=I next if K=0 then H=F else K=0 endif next G=B[E]-B[E-H]-1 for L=1 to A*H B[E]=B[E-H]+G:E=E+1 next G=0:H=0 next next print A 例 0,1,2,3,2,3 0,1,2,3,2,2,3,4,5,4
S(x).超数列を強化.
バシク行列数(Bashicu matrix number)
A=9:dim B[∞,∞],C[∞,∞],D[∞] for E=0 to 9 for F=0 to A B[1,F]=1:C[1,F]=1 next for G=1 to 0 step -1 A=A*A for H=0 to G if H=0 then I=G:J=F else I=G-K+H:J=0 for L=J to F for M=0 to F D[M]=0:C[H+2,M]=0 next for N=0 to I for O=0 to L if B[I-N,O]<B[I,O]-D[O] | B[I,0]=0 then if B[I,O+1]=0 & H=0 then K=N:N=I:O=L elseif O=L & N<H+1 if C[H+1-N,L]=1 then C[H+1,L]=1 N=I else D[O]=B[I,O]-B[I-N,O] endif else O=L endif next next next next for P=0 to F if 0<B[G,P+1] then D[P]=B[G,P]-B[G-K,P] next for Q=1 to A for R=1 to K for S=0 to F if C[R,S]=1 then B[G,S]=B[G-K,S]+D[S] else B[G,S]=B[G-K,S] next G=G+1 next next next next print A 例 (0,0,0)(1,1,1)(2,1,0)(1,1,1) (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,2,0)
Bm(x).バシク行列数は512文字以内に定義されている.
バシク数 (0,0,0)(1,1,1)(2,2,0)(1,0,0)[3]
オメガバシク数 (0,0,0)(1,1,1)(2,2,2)(1,0,0)[3]
トリオ数列数 (0,0,0,0)(1,1,1,1)(1,0,0,0)[3]
バシク階差行列数(Bashicu Difference matrix number)
バシク超行列数(Bashicu hyper matrix number)
A=99:dim B[∞,∞],B2[∞,∞],C[∞],C2[∞]:C3[∞] for D=0 to 99 for D2=1 to A B[2,D2]=1 next for D3=2 to 1 step -1 A=pow(A,A) for D4=1 to D2 if 0<B[D3,D4] & B[D3,D4+1]=0 then for D5=0 to D3-1 for D6=1 to D4 if 0<B[D3-D5,D6]<B[D3,D6]-C[D6] then if D6<D4 then C[D6]=B[D3,D6]-B[D3-D5,D6] else if D7=0 then D7=D5 D8=D8+1 C2[D8]=D5 for D9=1 to D6 B2[D3-D5,D9]=D8 next for D10=1 to D4 for D11=D3-D5 to D3 for D12=D11 to D3-D5 step -1 for D13=1 to D10 if B[D12,D13]<B[D11,D13]-C3[D13] then if D10=D13 then if 0<B2[D12,D10] & B2[D11,D10]=0 then B2[D11,D10]=D8 D12=D3-D5 else C3[D13]=B[D11,D13]-B[D12,D13] endif else D13=D10 endif next next for D14=1 to D2 C3[D14]=0 next next next for D15=0 to D7 for D16=1 to D2 D17=0 if 0<B2[D3-D7+D15,D16] then if D16<D4 then D17=B[D3-C2[B2[D3-D7+D15,D16]],D16]-B[D3-D5,D16] endif if B[D3-D5+D15,D16]<B[D3-D7+D15,D16]-D17 then D15=D7:D16=D2:D18=1:D5=D3:D8=D8-1 elseif B[D3-D7,D16]-D17<B[D3-D5,D16] D15=D7:D16=D2 endif next next if D18=0 then D19=D5 else D18=0 endif else D6=D4 endif next next D4=D2 endif next for D20=1 to D2 if 0<B[D3,D20+1] then C[D20]=B[D3,D20]-B[D3-D19,D20] next for D21=1 to A*D19 for D22=1 to D2 if 0<B2[D3-D19,D22] & B2[D3-D19,D22]<D8+1 then B[D3,D22]=B[D3-D19,D22]+C[D22]:B2[D3,D22]=B2[D3-D19,D22] else B[D3,D22]=B[D3-D19,D22] next D3=D3+1 next for D23=1 to D3 for D24=1 to D2 B2[D23,D24]=0 next next D7=0:D8=0:D19=0 for D25=1 to D2 C[D25]=0 next next next print A 例 (0,0,0)(1,1,1)(2,2)(3) (0,0,0)(1,1,1)(2,2)(2,2) (0,0,0)(1,1,1)(2,2)(2,1,1)(3,2) (0,0,0)(1,1,1)(2,2)(2,1,1)(3,1,1)(4,2)(5,1,1)
バシク行列=(0,0,0)(1,1,1)(1,1,0)(1,0,0)(2).超数列の一般化.
バシク急行列数(Bashicu sudden matrix number)
A=999:dim B[∞,∞],B2[∞,∞],C[∞],C2[∞],C3[∞] for D=0 to 999 for D2=1 to A B[2,D2]=1 next for D3=2 to 1 step -1 A=Bas(A,A,A) for D4=1 to D2 if 0<B[D3,D4] & B[D3,D4+1]=0 then for D5=0 to D3-1 for D6=1 to D2 if B[D3-D5,D6]<B[D3,D6]-C[D6] then if D6<D4 then C[D6]=B[D3,D6]-B[D3-D5,D6] else if D7=0 then D8=D5 D9=D9+1 if C[D4]+1<B[D3,D6]-B[D3-D5,D6] then C[D4]=C[D4]+1 C2[D9]=D5 for D10=1 to D4 B2[D3-D5,D10]=D9 next for D11=1 to D4 for D12=D3-D5+1 to D3 for D13=D12 to D3-D5 step -1 for D14=1 to D11 if B[D13,D14]<B[D12,D14]-C3[D14] then if D11=D14 then if 0<B2[D13,D11] & B2[D12,D11]=0 then B2[D12,D11]=D9 D13=D3-D5 else C3[D14]=B[D12,D14]-B[D13,D14] endif else D14=D11 endif next next for D15=1 to D4 C3[D15]=0 next next next for D16=0 to D8 for D17=1 to D2 D18=0 if 0<B2[D3-D8+D16,D17] then if D17<D4+1 then D18=B[D3-C2[B2[D3-D8+D16,D17]],D17]-B[D3-D5,D17] endif if B[D3-D5+D16,D17]<B[D3-D8+D16,D17]-D18 then D16=D7:D17=D2:D19=1:D5=D3:D9=D9-1 elseif B[D3-D8+D16,D17]-D18<B[D3-D5+D16,D17] D16=D7:D17=D2 endif next next if D19=0 then D7=D5 else D19=0 endif else D6=D4 endif next next D4=D2 endif next for D20=1 to D2 if 0<B[D3,D20+1] then C[D20]=B[D3,D20]-B[D3-D7,D20] else C[D20]=B[D3,D20]-B[D3-D7,D20]-1:D20=D2 next for D21=1 to A*D7 for D22=1 to D2 if 0<B2[D3-D7,D22] & B2[D3-D7,D22]<D9+1 then B[D3,D22]=B[D3-D7,D22]+C[D22]:B2[D3,D22]=B2[D3-D7,D22] else B[D3,D22]=B[D3-D7,D22] next D3=D3+1 next for D23=1 to D3 for D24=1 to D2 B2[D23,D24]=0 next next D7=0:D8=0:D9=0 for D25=1 to D2 C[D25]=0 next next next print A 例 (0,0)(1,1)(2,1)(3,0) (0,0)(1,1)(2,1)(2,1)(3,1)(3,1)(4,1)
Bsm(x).基本関数はバシク関数とする.急数列の一般化,