43 lines
2.0 KiB
Plaintext
43 lines
2.0 KiB
Plaintext
For this task, the Stern-Brocot sequence is to be generated by an algorithm similar to that employed in generating the [[Fibonacci sequence]].
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# The first and second members of the sequence are both 1:
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#* 1, 1
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# Start by considering the second member of the sequence
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# Sum the considered member of the sequence and its precedent, (1 + 1) = 2, and append it to the end of the sequence:
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#* 1, 1, 2
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# Append the considered member of the sequence to the end of the sequence:
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#* 1, 1, 2, 1
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# Consider the next member of the series, (the third member i.e. 2)
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# GOTO 3
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#*
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#* ─── Expanding another loop we get: ───
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#*
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# Sum the considered member of the sequence and its precedent, (2 + 1) = 3, and append it to the end of the sequence:
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#* 1, 1, 2, 1, 3
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# Append the considered member of the sequence to the end of the sequence:
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#* 1, 1, 2, 1, 3, 2
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# Consider the next member of the series, (the fourth member i.e. 1)
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;The task is to:
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* Create a function/method/subroutine/procedure/... to generate the Stern-Brocot sequence of integers using the method outlined above.
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* Show the first fifteen members of the sequence. (This should be: 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4)
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* Show the (1-based) index of where the numbers 1-to-10 first appear in the sequence.
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* Show the (1-based) index of where the number 100 first appears in the sequence.
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* Check that the greatest common divisor of all the two consecutive members of the series up to the 1000<sup>th</sup> member, is always one.
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<br>Show your output on this page.
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;Related tasks:
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:* [[Fusc sequence]].
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:* [[Continued fraction/Arithmetic]]
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;Ref:
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* [https://www.youtube.com/watch?v=DpwUVExX27E Infinite Fractions - Numberphile] (Video).
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* [http://www.ams.org/samplings/feature-column/fcarc-stern-brocot Trees, Teeth, and Time: The mathematics of clock making].
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* [https://oeis.org/A002487 A002487] The On-Line Encyclopedia of Integer Sequences.
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<br><br>
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