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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 256 34 "3n+1 Conjecture or Colla
tz Problem" }}{PARA 19 "" 0 "" {TEXT -1 10 "Yonggu Kim" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 257 78 "The follwoing procedure T gives the definition of the 3n
+1 conjecture funtion." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "
T:=proc(n::nonnegint)\n  if type(n,odd) then\n           (3*n+1)/2;\n \+
 else     n/2;\n  end if\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "T(6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "T(5);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\")" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 258 39 "The ne
xt procedure TT(n,m) is equal to " }{XPPEDIT 259 0 "T^m;" "6#)%\"TG%\"
mG" }{TEXT 260 31 "(n), that is, T(T(...T(n)...))." }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 135 "TT:=proc(n::nonnegint,m::nonnegint)\n     \+
local i, k;\n     k:=n;\n     for i from 1 to m do\n     k:= T(k);\n  \+
   end do;\n     k;\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 9 "TT(15,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#`" }}}{EXCHG }
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "seq(TT(15,k),k=1..20);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "66\"#B\"#N\"#`\"#!)\"#S\"#?\"#5\"\"&\"\"
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TT(21,k),k=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6,\"#K\"#;\"\")\"
\"%\"\"#\"\"\"F'F(F'F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "s
eq(TT(23,k),k=1..20);" }}{PARA 11 "" 1 "" {XPPMATH 20 "66\"#N\"#`\"#!)
\"#S\"#?\"#5\"\"&\"\")\"\"%\"\"#\"\"\"F,F-F,F-F,F-F,F-F," }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "seq(TT(115,k),k=1..30);" }}{PARA 
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\"#G\"#9\"\"(\"#6\"#<\"#E\"#8\"#?\"#5\"\"&\"\")\"\"%\"\"#\"\"\"F8F9F8F
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#<\"#E\"#8\"#?\"#5\"\"&\"\")\"\"%\"\"#\"\"\"F0F1F0F1F0" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 261 82 "In the following procedure, TC counts th
e smallest number m such that TT(n,m) = 1." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 159 "TC:=proc(n::nonnegint)\n     local k, m;\n     k:=
1;\n     m:=T(n);\n     while not m = 1 do\n           k:=k+1;\n      \+
     m:=T(m);\n     end do;\n     k; \nend proc:" }}}{EXCHG {PARA 0 ">
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