{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 24 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple O utput" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Time s" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 256 21 "Conjectura de Collatz" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 256 "" 0 "" {TEXT 258 75 "\"come\347ando com um inteiro n qualq uer, se iterarmos sucessivamente a fun\347\343o " }}{PARA 256 "" 0 "" {TEXT 259 51 "f(n)=n/2 (se n \351 par) ou f(n)=3n+1 (se n \351 \355mpa r), " }}{PARA 256 "" 0 "" {TEXT 260 60 "chegaremos sempre a 1 ao cabo \+ de um n\372mero finito de passos\"" }}{PARA 256 "" 0 "" {TEXT -1 1 " \+ " }{TEXT 257 0 "" }{TEXT -1 0 "" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 43 "Procedimento que define a fun \347\343o de Collatz" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Collatz := proc(n::integer)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " if type(n,even) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " n/2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " el se" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " 3*n+1;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 " fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 85 "Procedimento de contagem das itera\347\365es sucessivas da fun \347\343o de Collatz at\351 chegar a 1" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "IC := proc(raiz::intege r)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 " local sentinela, contador; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " contador := 0;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 " sentinela := raiz;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " while sentinela <> 1 and contador < 1000^1000 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " sentinela := Collatz(senti nela);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 " contador := contad or + 1;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 " od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " RETURN(contador);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }} {PARA 257 "" 0 "" {TEXT -1 56 "Verifica\347\343o da conjectura para os primeiros 200 inteiros" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "seq(IC(i), i=1..200);" }}{PARA 12 " " 1 "" {XPPMATH 20 "6dw\"\"!\"\"\"\"\"(\"\"#\"\"&\"\")\"#;\"\"$\"#>\" \"'\"#9\"\"*F.\"#\"Fd oFdoF9F9F9FdoF9" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 261 61 "Procedimento que calcula a sequ\352n cia n, f(n), f(f(n)), ..., 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "sCollatz := proc(n::integer)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 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