BASIC言語による巨大数のまとめ

原始数列数・一次数列数(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

P(x)=f_{ε_0}(x)

大一次数列数(Large primitive sequence number)

A=9:dim B[∞]
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

Lp(x)=f_{φ(ω,0)}(x)

原始数列の簡単な拡張

ペア数列数・二次数列数(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]
     B[F-G]<B[F] then I=G:G=F
   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

Pair(x)=f_{Ψ_Ω(Ω_ω)}

バシク行列数(Bashicu matrix number)

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

バシク三角行列数(Bashicu triangular matrix number)

A=99:dim B[∞,∞],C[∞,∞],D[∞]
for E=0 to 99
 for F=1 to A
  B[F,1]=F:C[F,1]=1
  for G=2 to F
   B[F,G]=1
  next
 next
 for H=A to 1 step -1
  A=pow(A,A)
  for I=1 to H-1
   for J=1 to F
    if B[H-I,J]<B[H,J]-D[J] then
     if B[H,J+1]=0 then
      if 1<B[H,J]-B[H-I,J] | (J=2 | K=1) & 0<B[H,J+1] then K=1 else L=I:M=J:I=H:J=F
     else
      if J=1 then D[J]=B[H,J]-B[H-I,J]
     endif
    else
     J=G
    endif
   next
  next
  for N=2 to L
   C[N,1]=1
   for O=2 to F
    for P=0 to H
     if B[H-L+N-P-1,1]<B[H-L+N-1,1] then
      if (C[N-P,O]=1 | 2<O & C[N,O-1]=1) & B[H-L,O]<B[H-L+N-1,O] & O<M then
       C[N,O]=1
      else
       C[N,O]=0
      endif
      P=H
     endif
    next
   next
  next
  for Q=0 to H-1
   if B[H-Q,1]<B[H,1] then
    if M<3 | K=1 then Q=0 elae S=1
    for R=1 to M-1
     D[R]=B[H-Q,R]-B[H-L,R]
    next
    Q=H
   endif
  next
  for T=1 to A
   for U=1+S to L
    for V=1 to F
     if C[U,V]=1 then B[H,V]=B[H-L+S,V]+D[V] else B[H,V]=B[H-L+S,V]
    next
    H=H+1
   next
  next
  K=0:L=0:S=0
  for W=1 to F
   D[W]=0
  next
 next
next
print A