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Ingy döt Net 2023-07-01 11:58:00 -04:00
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The '''[[wp:Recamán's sequence|Recamán's sequence]]''' generates Natural numbers.
Starting from a(0)=0, the n'th term <code>a(n)</code>, where n>0, is the previous term minus <code>n</code> i.e <code>a(n) = a(n-1) - n</code> but only if this is '''both''' positive ''and'' has not been previousely generated.<br>
If the conditions ''don't'' hold then <code>a(n) = a(n-1) + n</code>.
;Task:
# Generate and show here the first 15 members of the sequence.
# Find and show here, the first duplicated number in the sequence.
# '''Optionally''': Find and show here, how many terms of the sequence are needed until all the integers 0..1000, inclusive, are generated.
;References:
* [https://oeis.org/A005132 A005132], The On-Line Encyclopedia of Integer Sequences.
* [https://www.youtube.com/watch?v=FGC5TdIiT9U The Slightly Spooky Recamán Sequence], Numberphile video.
* [https://en.wikipedia.org/wiki/Recam%C3%A1n%27s_sequence Recamán's sequence], on Wikipedia.
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