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巨大数研究 Wiki

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BASIC言語による巨大数のまとめ

2014

原始数列、ペア数列、トリオ数列→バシク行列

2015

原始数列→小一次数列、大一次数列 

ペア数列、大一次数列→三角一次数列

大一次数列、バシク行列→大バシク行列

バシク行列→バシク数列

2016

バシク数列→小バシク数列

2017

小バシク数列、バシク行列→バシク三角行列

小一次数列→第二小一次数列、零次数列数

大きさ

零次数列<小一次数列<第二小一次数列<原始数列<大一次数列<ペア数列≦三角一次数列<小バシク数列≦トリオ数列<バシク行列<大バシク行列<バシク数列<バシク三角行列

零次数列数(Zero dimensional sequence number)

A=9
for B=0 to 9
 for C=A to 0 step -1
  A=A*A
 next
next
print A

\(Z_1=9^{1024}\)、\(Z_{n+1}=Z_n^{2^{Z_n+1}}\)としたときの\(Z_{10}\)に一致。

小一次数列数(Small primitive sequence number)

A=9:dim B[infinity]
for C=0 to 9
  B[0]=A
  for D=0 to 0 step -1
    A=A*A
    E=B[D]
    for F=0 to A
     if 0<E then B[D]=E-1:D=D+1
    next
  next
next
print A

\(H_{ω^{ω+1}}(10)\)に相当。

第二小一次数列数(Second small primitive sequence number)

A=9:dim B[infinity]
for C=0 to 9
 B[0]=A
 for D=0 to 0 step -1
  A=A*A
  for E=0 to D
   if B[E+1]<=B[E] | B[E]=0 then
    if B[E]=0 then F=E:G=1:E=D
   else
    E=D
   endif
  next
  if G=1 then
   if 1<F then
    B[F]=B[F-1]:B[F-1]=B[F]-1:H=D-F+1
    for I=1 to A
     for J=0 to H
      B[D+1-J]=B[D-J]
     next
     D=D+1
    next
    D=D+1
   else
    for K=2 to D
     B[K-1]=B[K]
    next
    B[D]=0
   endif
  else
   for L=1 to A
    for M=0 to D
     if B[M]=L & (L<B[M+1] | M=D) then O=M:P=1:M=D
    next
    if P=1 then L=A
   next
   Q=D-O:B[O]=B[O]-1
   for R=1 to A
    for S=0 to Q
     B[D+1-T]=B[D-T]
    next
    D=D+1
   next
   D=D+1
  endif
  G=0:P=0
 next
next
print A

\(f_{ω^ω+1}(10)\)に相当。

原始数列数(Primitive sequence number)

A=9:dim B(infinity)
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

\(f_{ε_0+1}\)(10)に相当。一次数列数とも呼ぶ。

大一次数列数(Large primitive sequence number)

A=9:dim B(infinity)
for C=0 to 9
  B(1)=A
  for D=1 to 0 step -1
    A=A*A
    for E=0 to D
      if B(D-E)<B(D) or B(D)=0 then F=E:E=D
    next
    G=B(D)-B(D-F)-1
    for H=1 to A*F
      B(D)=B(D-F)+G:D=D+1
    next
  next
next
print A

\(f_{φ(ω,0)+1}(10)\)に相当。

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 C
   if A[F]=0 | (A[F-G]<A[F] & (B[F]=0 | B[F-G]<B[F])) then H=G:G=C
  next
  if B[F]=0 then I=0 else I=A[F]-A[F-H]
  for J=1 to C*H
   A[F]=A[F-H]+I:B[F]=B[F-H]:F=F+1
  next
 next
next
print C

\(f_{ψ_Ω(Ω_ω)+1}(10)\)に相当。二次数列数ともよぶ。

三角一次数列数(Triangular primitive sequence number)

A=9:dim B(infinity):dim C(infinity)
for D=0 to 9
  for E=1 to A
    B(E)=B(E-1)+E
  next
  for F=A to 0 step -1
    A=A*A
    for G=0 to F
      for H=G to F
        if B(F-H)<B(F-G) then C(F-G)=B(F-G)-B(F-H):H=F        
      next
      if B(F-G)=0 then C(F-G)=1
      if B(F)=0 or (B(F-G)<B(F) and (C(F-G)<C(F) or C(F)=1)) then I=G:G=F
    next
    J=B(F)-B(F-I)-1
    for K=1 to I*A
      B(F)=B(F-I)+J:F=F+1
    next
  next
next
print A

\(f_{ψ_Ω(Ω_ω)+1}(10)\)に相当。

小バシク数(Small bashicu number)

A=9:dim B[∞],C[∞],D[∞],E[∞],F[∞],G[∞,∞]
for H=0 to 9
 for I=1 to A
  for J=1 to I
   K=K+1:B[K]=I*I-2*(I-J)
  next
 next
 for K=K to 1 step -1
  A=A*A
  for I=0 to K
   for J=I to K then
    if B[I]<B[J] then C[J]=B[J]-B[I]:L=K-I
    endif
   next
  next
  if C[K]+C[K-L]=2 then
   for I=1 to A*L
    B[K]=B[K-L]:K=K+1
   next
  else
   for I=1 to K
    if B[K-I]<B[K] & C[K-I]=1 then J=I:I=K
   next
   for I=1 to K
    if B[K-I]=B[K-J]+int((B[K]-B[K-J])/2)*2 then
     L=0
     for M=K-I+1 to K
      if B[M]-B[K-I]<3 then L=L+1:D[L]=0:N=1
      D[L]=D[L]+(B[M]-B[K-I])*pow(A,A-N):N=N+1
     next
     M=J:O=J:P=0
     for Q=J to K
      if B[K-Q]<B[K-M] & C[K-Q]=1 then
       for R=1 to K
        if B[K-R]=B[K-Q]+int((B[K]-B[K-J])/2)*2 then
         for S=0 to J-I
          if B[K-Q+S]-B[K-Q]=B[K-J+S]-B[K-J] then T=1 else T=0:S=J
         next
         if T=1 then
          for R=R+1 to O-1
           if B[K-R]-E[P]<3 then S=S+1:G[N,S]=0:T=1
           G[P,S]=G[P,S]+(B[K-R]-E[P])*pow(A,A-T):T=T+1
          next
          F[P]=S:G[P,S+1]=0
          if Q-R=J-L then
           M=Q:O=R
           for S=1 to L
            if G[P,S]<D[S] | G[P,S]<2*pow(A,A-1) then Q=K:S=L
           next
          else
           M=Q
          endif
          R=K
         endif
        endif
       next
      endif
     next
     for Q=1 to P
      for R=F[Q] to 0 step -1
       if R=0 | D[L]-mod(D[L],pow(A,A-N+2))<G[Q,R] then
        G[Q,R+1]=0-D[L]+mod(D[L],pow(A,A-N+2)):R=0
       else
        G[Q,R+1]=G[Q,R]
       endif
      next
     next
     if 0<G[P,Q+1] then F[P]=F[P]+1
     K=K-I:J=B[K-J]-B[K-M]:M=M-I:O=M-O
     for Q=1 to A
      for R=1 to O
       B[K]=B[K-M]+J:K=K+1
      next
      M=O
      for R=P to 1 step -1
       E[R]=E[R]+J
       for S=1 to F[R]
        if G[R,T]<0 then S=Q else S=1
        for T=1 to S
         for U=0 to A
          V=mod(abs(G[R,S]),pow(A,A-U)))
          if V=0 then U=A else B[K]=int(V/pow(A,A-U-1))+E[S]:K=K+1:M=M+1
         next
        next
       next
      next
     next
     I=K
    endif
   next
  endif
 next
next
print A

\(ψ_Ω(ψ_I(0))\)程度のシステムを編み出す際にできたシステム。平方充填列数(Square filling sequence number)とも呼ぶ。トリオ数列と同じくらいの強さ?

トリオ数列数(Trio sequence number)

A=9:dim B[∞],C[∞],D[∞],E[∞],F[∞]
for G=0 to 9
 for H=0 to A
  B[H]=H:C[H]=H:D[H]=H
 next
 E[1]=1:F[1]=1
 for I=A to 0 step -1
  A=A*A
  for J=0 to I
   if B[I-J]<B[I]-K | B[I]=0 then
    if 0<C[I] then K=B[I]-B[I-J]
    if C[I-J]<C[I]-L | C[I]=0 then
     if 0<D[I] then L=C[I]-C[I-J]
     if D[I-J]<D[I] | D[I]=0 then M=J:J=I
    endif
   endif
  next
  for N=1 to M
   for O=N to 0 step -1
    if B[I-M+O]<B[I-M+N] then
     if B[I-M]<B[I-M+O] & E[O+1]=1 then E[N+1]=1 else E[N+1]=0
     if C[I-M]<C[I-M+O] & F[O+1]=1 then F[N+1]=1 else F[N+1]=0
     O=0
    endif
   next
  next
  for P=1 to A
   for Q=1 to M
    B[I]=B[I-M]:C[I]=C[I-M]:D[I]=D[I-M]
    if E[Q]=1 then B[I]=B[I]+K
    if F[Q]=1 then C[I]=C[I]+L
    I=I+1
   next
  next
  K=0:L=0
 next
next
print A

三次数列数とも呼ぶ。この辺から計算が終わるかが不明。

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
   for I=0 to F
    if B[G-H,I]<B[G,I]-D[I] | B[G,0]=0 then
     if B[G,I+1]=0 then I=F:J=H:H=G else D[I]=B[G,I]-B[G-H,I]
    else
     I=F
    endif
   next
  next
  for K=1 to J
   for L=K to 0 step -1
    if B[G-J+L,0]<B[G-J+K,0] then
     for M=0 to F
      if B[G-J,M]<B[G-J+K,M] & C[L+1,M]=1 then C[K+1,M]=1 else C[K+1,M]=0
     next
     L=0
    endif
   next
  next
  for N=1 to A
   for O=1 to J
    for P=0 to F
     B[G,P]=B[G-J,P]
     if C[O,P]=1 then B[G,P]=B[G,P]+D[P]
    next
    G=G+1
   next
  next
  for Q=1 to F
   D[Q]=0
  next
 next
next
print A

原始数列、ペア数列、トリオ数列を一般化したバシク行列システムで定義される巨大数。

大バシク行列数(Large bashicu matrix number)

A=9:dim B[∞,∞],C[∞,∞],D[∞]
for E=0 to 9
  B[1,0]=A:C[1,0]=1:F=2
 for G=1 to 0 step -1
  A=A*A
  for H=0 to G
   for I=0 to F
    if B[G-H,I]<B[G,I]-D[I] | B[G,1]=0 then
     if B[G,I+1]=0 then I=F:J=H:H=G else D[I]=B[G,I]-B[G-H,I]
    else
     I=F
    endif
   next
  next
  for K=1 to J
   for L=K to 0 step -1
    if B[G-J+L,0]<B[G-J+K,0] then
     for M=0 to F
      if B[G-J,M]<B[G-J+K,M] & C[L+1,M]=1 then C[K+1,M]=1 else C[K+1,M]=0
     next
     N=B[G-J+K,M]-B[G-J,M]
     L=0
    endif
   next
  next
  if 1<N & 0<J then
   B[G,0]=B[G,0]-1
   for N=1 to A
    B[G,N]=B[G,N]+1
   next
   F=A+1:G=G+1
  else
   for N=1 to A
    for O=1 to J
     for P=0 to F
      B[G,P]=B[G-J,P]
      if C[O,P]=1 then B[G,P]=B[G,P]+D[P]
     next
     G=G+1
    next
   next
  endif
  for Q=1 to F
   D[Q]=0
  next
 next
next
print A

大一次数列をベースにしたバシク行列の簡単な拡張。一行目の要素にラベルを付けるなど、さらなる発展も考えられる。

バシク数(Bashicu number)

A=9:dim B[∞],C[∞],D[∞],E[∞],F[∞],G[∞],H[∞],I[∞,∞],J[∞,∞]
for K=0 to 9
for L=1 to A
  for M=1 to L
   N=N+1:B[N]=L*L-2*(L-M)
  next
next
for N=N to 1 step -1
  A=A*A
  for O=0 to N
   for P=O to N
    if B[O]<B[P] then C[P]=B[P]-B[O]:Q=P-O
   next
  next
  if C[N]+C[N-Q]=2
   for O=1 to A*Q
    B[N]=B[N-Q]:N=N+1
   next
  else
   O=B[N]
   for P=1 to N
    if B[N-P]<O then
     if C[N-P]=1 then O=P:P=N else O=B[N-P]
    endif
   next
   for P=1 to N
    if B[N-P]=B[N-O]+int((B[N]-B[N-O])/2)*2 then
     Q=0
     for R=N-P+1 to N
      if B[R]-B[N-P]<3 then Q=Q+1:S=1:D[Q]=0:E[Q]=0
      D[Q]=D[Q]+(B[R]-B[N-P])*pow(A,A-S):E[Q]=E[Q]+C[R]*pow(A,A-S):S=S+1
     next
     for R=Q to 2 step -1
      if D[R]<D[P-1] | E[R]<E[R-1] then S=D[R]:D[R]=D[R-1]:D[R-1]=S:S-0
     next
     if S=0 then
      N=N-P+1
      for P=1 to 1 to Q
       for R=0 to A
        S=mod(D[P],pow(A,A-R))
        if S=0 then R=A else B[N]=int(S/pow(A,A-R-1))+B[N-T]:N=N+1
       next
      next
     else
      P=B[N-O]:R=O:S=0:T=0
      for U=O to N
       if B[N-U]<P then
        if C[N-U]=1 then
         for V=R to N
          if B[N-V]=B[N-U]+int((B[N]-B[N-O])/2)*2 then
           S=S+1:F[S]=B[N-V]:W=0
           for X=V+1 to R-1
            if B[N-X]-F[S]<3 then W=W+1:Y=1:I[S,W]=0:J[S,W]=0
            I[S,W]=I[S,W]+(B[N-X]-F[S])*pow(A,A-Y):J[S,W]=J[S,W]+C[N-X]*pow(A,A-Y):Y=Y+1
           next
           G[S]=W:R=V:V=N:W=0:X=0
          endif
         next
         for V=0 to A
          for Y=1 to Q
           if V<D[Y] then W=W+1
          next
          for Y=1 to S
           if V<I[S,Y] & 2*pow(A,A-1)<=I[S,Y] then W=W-1
          next
          if 0<W then X=X+1 else A
         next
         for V=Q to 1 step -1
          if D[V]=X then T=T+1:H[T]=D[V]:C[T]=E[V]:D[V]=0
         next
         if D[Q]=0 then R=R-U:Q=U:U=N
        endif
        P=B[N-U]
       endif
      next
      for U=1 to A
       if mod(H[T],pow(A,A-U))=0 then H[T]=H[T]-mod(H[T],pow(A,A-U+1)):U=A
      next
      if H[T]=0 then T=T-1
      for U=1 to S
       for V=1 to T
        for W=G[O] to 0 step -1
         if W=0 then
          I[U,1]=0-H[V]:G[U]=G[U]+1
         else
          if H[V]<=I[U,W] | C[V]<J[U,W] | I[U,W]<pow(A,A-1)*2 then
           I[U,W+1]=I[U,W]
          else
           I[U,W+1]=0-H[V]:G[U]+1:W=0
          endif
         endif
        next
       next
      next
      N=N-O:P=B[N]-P:Q=Q-O
      for O=1 to A
       for T=1 to R
        B[N]=B[N-Q]+P:N=N+1
       next
       Q=R
       for T=S to 1 step -1
        F[T]=F[T]+P
        for U=1 to G[T]
         if I[T,U]<0 then V=O else V=1
         for W=1 to T
          for X=0 to A
           Y=mod(abs(I[T,U]),pow(A,A-X))
           if Y=0 then X=A else B[N]=int(Y/pow(A,A-X-1))+F[T]:N=N+1:Q=Q+1
          next
         next
        next
       next
      next
     endif
     P=N
    endif
   next
  endif
 next
next
print A

バシク行列の行数をω以上に拡張し、発展させて行列自体を入れ子になどしたシステム。

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