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Search: id:A093903
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| A093903 |
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a(1) = 1; for n > 1, a(n) = a(n-1)-p if there exists a prime p (take the smallest) that has not yet been used and is such that a(n) is new and > 0, otherwise a(n) = a(n-1)+p if the same conditions are satisfied. |
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9
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| 1, 3, 6, 11, 4, 15, 2, 19, 38, 9, 32, 63, 26, 67, 24, 71, 18, 77, 16, 83, 12, 85, 164, 81, 170, 73, 174, 65, 168, 61, 188, 75, 206, 69, 208, 59, 210, 53, 216, 49, 222, 43, 224, 33, 226, 29, 228, 17, 240, 13, 242, 475, 236, 477, 220, 471, 202, 465, 194, 487, 204, 481, 200
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A variation of Cald's sequence A006509; a sequence of distinct positive integers with property that absolute successive differences are distinct primes.
A more long-winded definition: Start with a(1) = 1. Keep a list of the primes that have been used so far; initially this list is empty. Each prime can be used at most once.
To get a(n), subtract from a(n-1) each prime p < a(n-1) that has not yet been used, starting from the smallest. If for any such p, a(n-1)-p is not yet in the sequence, set a(n) = a(n-1)-p and mark p as used.
If no p works, then add each prime p that has not yet been used to a(n-1), again starting with the smallest. When p is such that a(n-1)+p is not yet in the sequence, set a(n) = a(n-1)+p and mark p as used. Repeat.
The main question is: does every number appear in the sequence?
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EXAMPLE
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1 -> 1+2 = 3, and prime 2 has been used.
3 -> 3+3 = 6, and prime 3 has been used.
6 could go to 6-5 = 1, except 1 is already in the sequence; so 6 -> 6+5 = 11, and prime 5 has been used.
11 -> 11-7 = 4 (for the first time we can subtract), and prime 7 has been used.
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CROSSREFS
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Similar to Cald's sequence A006509 and Recaman's sequence A005132. Differs from A006509. Cf. A094746 (the primes associated with this sequence), A113959 (where n appears), A113960, A113961, A113962.
Sequence in context: A079801 A083462 A110080 this_sequence A117128 A006509 A102889
Adjacent sequences: A093900 A093901 A093902 this_sequence A093904 A093905 A093906
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 24 2004
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EXTENSIONS
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Definition (and sequence) corrected by R. Piyo (nagoya314(AT)yahoo.com) and njas, Dec 09 2004
Edited, offset changed to 1, a(16) and following terms added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 10 2005
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