27 lines
1.2 KiB
Text
27 lines
1.2 KiB
Text
These two sequences of positive integers are defined as:
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:::: <big><math>\begin{align}
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R(1)&=1\ ;\ S(1)=2 \\
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R(n)&=R(n-1)+S(n-1), \quad n>1.
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\end{align}</math></big>
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<br>
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The sequence <big><math>S(n)</math></big> is further defined as the sequence of positive integers '''''not''''' present in <big><math>R(n)</math></big>.
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Sequence <big><math>R</math></big> starts:
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1, 3, 7, 12, 18, ...
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Sequence <big><math>S</math></big> starts:
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2, 4, 5, 6, 8, ...
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;Task:
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# Create two functions named '''ffr''' and '''ffs''' that when given '''n''' return '''R(n)''' or '''S(n)''' respectively.<br>(Note that R(1) = 1 and S(1) = 2 to avoid off-by-one errors).
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# No maximum value for '''n''' should be assumed.
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# Calculate and show that the first ten values of '''R''' are:<br> 1, 3, 7, 12, 18, 26, 35, 45, 56, and 69
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# Calculate and show that the first 40 values of '''ffr''' plus the first 960 values of '''ffs''' include all the integers from 1 to 1000 exactly once.
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;References:
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* Sloane's [http://oeis.org/A005228 A005228] and [http://oeis.org/A030124 A030124].
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* [http://mathworld.wolfram.com/HofstadterFigure-FigureSequence.html Wolfram MathWorld]
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* Wikipedia: [[wp:Hofstadter_sequence#Hofstadter_Figure-Figure_sequences|Hofstadter Figure-Figure sequences]].
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<br><br>
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