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1. Commit library tape images, directories, and extracted text files. 2. Commit additional utilities under Unisys-Emode-Tools.
99 lines
7.8 KiB
Plaintext
99 lines
7.8 KiB
Plaintext
RD SEQUENCES OF NUMBERS ARE LISTS OF NUMBERS THAT ARE MADE 00000100
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UP WITH A PATTERN; IF YOU LOOK AT THE FIRST FEW NUMBERS, 00000200
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AND CAN FIGURE OUT HOW THE NUMBERS ARE RELATED TO EACH 00000300
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OTHER, OR HOW EACH NUMBER IS FORMED FROM THOSE THAT GO 00000400
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BEFORE IT, YOU HAVE CRACKED THE "CODE" OF THE SEQUENCE. 00000500
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00000600
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FOR EXAMPLE, THE SEQUENCE 2,4,6,8... IS FORMED BY ADDING 00000700
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TWO TO EACH NUMBER TO GET THE FOLLOWING NUMBER, OR YOU MAY 00000800
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THINK OF IT AS COUNTING BY TWO. 00000900
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PRESS THE LEFT ARROW KEY WHEN YOU ARE READY TO CONTINUE. 00001000
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QU DO YOU KNOW WHAT A SEQUENCE IS. 00001100
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CA NO 00001200
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CB I DO NOT 00001300
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TY IN A SEQUENCE THERE IS A RULE FOR FORMING EACH NEW 00001400
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NUMBER FROM THE PRECEDING NUMBERS, AND YOU HAVE TO FIND 00001500
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THE RULE. FOR EXAMPLE IN THIS SEQUENCE 1, 2, 4, 8, 16, ... 00001600
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EACH NUMBER IS OBTAINED FROM THE PRECEDING NUMBER BY 00001700
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DOUBLING IT. SOMETIMES THE RULE FOR FORMING THE SEQUENCE 00001800
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MAY BE STATED IN VARIOUS WAYS--THE EXAMPLE HERE MAY BE 00001900
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THOUGHT OF AS POWERS OF 2. 00002000
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CA YES 00002100
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CB OF COURSE 00002200
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BR PROB3 0000000T00002300
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UN PLEASE TYPE YES OR NO 00002400
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LA BACK 00002500
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QU THE RULE FOR FORMING THE SEQUENCE 1, 2, 3, 4, 5,... 00002600
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IS ADD ONE. WRITE A SEQUENCE STARTING WITH ONE IN 00002700
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WHICH YOU DOUBLE EACH NUMBER AND ADD ONE TO GET THE 00002800
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NEXT NUMBER. WRITE THE FIRST THREE TERMS, SEPARATING 00002900
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TERMS WITH COMMAS. 00003000
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CA 1, 3, 7 00003100
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CB 1,3,7 00003200
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CB 1,3,7, 00003300
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CB 1, 3, 7, 00003400
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CB ONE, THREE, SEVEN, 00003500
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CB ONE, THREE, SEVEN 00003600
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TY VERY GOOD. THE FIRST THREE NUMBERS ARE 1,3,7, AND IF 00003700
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SEVERAL MORE NUMBERS WERE GIVEN THE SEQUENCE WOULD LOOK 00003800
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LIKE THIS 1, 3, 7, 15, 31, 63, 127, ... 00003900
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THREE DOTS ARE PLACED AT THE END OF THE SEQUENCE TO SHOW 00004000
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THAT IT CONTINUES IN THE SAME PATTERN WITHOUT END. 00004100
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ANOTHER EXAMPLE IS* 1,1,2,3,5,8,13,... 00004200
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THERE ARE ESPECIALLY INTERESTING SEQUENCES, LIKE THE 00004300
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ONE ABOVE WHICH IS CALLED A FIBONACCI SEQUENCE AND HAS 00004400
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MANY INTERPRETATIONS IN NATURE. HOWEVER, FOR THE PRESENT 00004500
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WE JUST WANT TO CREATE PATTERNS AND SEE HOW YOU 00004600
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UNDERSTAND THEM. 00004700
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UN WRITE THE FIRST THREE NUMERALS IN THE SEQUENCE; EACH 00004800
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NUMERAL FOLLOWED BY A COMMA AND A SPACE. 00004900
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UN YOU WILL BE TAKEN BACK FOR A REVIEW OF SEQUENCES 00005000
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BR BACK 0000000H00005100
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LA PROB3 00005200
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QU HERE IS AN INTERESTING ONE: 1, 4, 9, 16, 25, 36, ... 00005300
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WHAT IS THE NEXT NUMBER IN THE SEQUENCE. 00005400
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CA 49 00005500
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CB FORTY-NINE 00005600
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CB FORTY NINE 00005700
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TY VERY GOOD. THE PATTERN CAN BE THOUGHT OF AS TAKING THE 00005800
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COUNTING NUMBERS, 1, 2, 3, 4, 5, 6, AND SO ON AND 00005900
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MULTIPLYING EACH NUMBER BY ITSELF OR AS SQUARING IT. 00006000
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UN TRY AGAIN. LOOK AT THE NUMBERS FOR A PATTERN. 00006100
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QU HERE IS ONE THAT IS VERY CLOSELY RELATED TO THE ONE 00006200
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ABOVE. 1, 8, 27, 64, ... WHAT IS THE NEXT NUMBER 00006300
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IN THE SEQUENCE. 00006400
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CA 125 00006500
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TY EXCELLENT. I AM SURE THAT YOU SEE THE PATTERN IS TO TAKE 00006600
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EACH COUNTING NUMBER AS A FACTOR THREE TIMES; OR TO CUBE 00006700
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EACH COUNTING NUMBER. 00006800
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UN TRY AGAIN. 00006900
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UN YOU DID NOT LOOK AT THE NUMBERS; THE FIRST ONE IS 1, 00007000
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THE SECOND NUMBER IS 8 WHICH EQUALS 2X2X2, THE THIRD 00007100
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NUMBER IS 27, WHICH IS 3X3X3, THE FOURTH NUMBER IS 00007200
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64 WHICH IS 4X4X4. NOW WHAT IS THE FIFTH NUMBER. 00007300
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UN IF YOU GIVE UP TYPE HELP. 00007400
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QU HERE IS A NEW ONE. 1, 4, 13, 40, 121, ... WHAT IS 00007500
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THE NEXT NUMBER IF YOU ARE TOLD THAT IN THIS SEQUENCE 00007600
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IT INVOLVED A MULTIPLICATION AND AN ADDITION. 00007700
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CA 364 00007800
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TY THAT IS CORRECT. YOU HAVE SEEN THAT THE RULE OR PATTERN 00007900
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IS TO MULTIPLY THE NUMBER BY THREE AND ADD ONE. 00008000
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UN THINK OF HOW EACH NUMBER IF FORMED FROM THE ONE BEFORE IT. 00008100
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WRITE YOUR ANSWER NOW. 00008200
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UN THE SEQUENCE IS 1, 4, 13, 40, 121, ... THINK ABOUT 00008300
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MULTIPLYING EACH NUMBER BY THREE AND ADDING SOMETHING. 00008400
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UN IF YOU GIVE UP TYPE HELP. 00008500
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QU THESE CAN BE DONE WITH FRACTIONS TOO. CAN YOU FIGURE 00008600
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THIS PATTERN: 1, 1/2, 1/4, ... WHAT WILL THE NEXT NUMBER BE. 00008700
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CA 1/8 00008800
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TY THAT IS CORRECT. YOU HAVE THE IDEA OF SEQUENCES AND CAN 00008900
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CREATE PATTERNS OF YOUR OWN AND TRY THEM OUT ON YOUR 00009000
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FRIENDS. 00009100
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00009200
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THIS IS THE END OF THIS COURSE. PLEASE REMEMBER WHAT YOU 00009300
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HAVE LEARNED. 00009400
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UN YOU ARE NOT THINKING 00009500
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UN LOOK AT THE DENOMINATORS. EACH NUMERATOR IS 1, BUT THE 00009600
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DENOMINATORS ARE CHANGING IN A VERY EASY WAY. 00009700
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99 00009800
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