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Search: id:A020703
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| A020703 |
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Take the sequence of natural numbers (A000027) and reverse successive subsequences of lengths 1,3,5,7,... |
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+0
2
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| 1, 4, 3, 2, 9, 8, 7, 6, 5, 16, 15, 14, 13, 12, 11, 10, 25, 24, 23, 22, 21, 20, 19, 18, 17, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 81, 80, 79, 78, 77
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Arrange A000027, the natural numbers, into a (square) spiral, say clockwise as shown in A068225. Read the numbers from the resulting counterclockwise spiral of the same shape that also begins with 1 and this sequence results. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Aug 04 2006
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REFERENCES
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R. Honsberger, "Ingenuity in Mathematics", Table 10.4 on page 87.
Suggested by correspondence with Michael Somos.
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LINKS
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Index entries for sequences that are permutations of the natural numbers
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PROGRAM
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(PARI) a(n)=local(t); if(n<1, 0, t=sqrtint(n-1); 2*(t^2+t+1)-n)
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CROSSREFS
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A self-inverse permutation of the natural numbers.
Cf. A000027, A038722.
Sequence in context: A132668 A018866 A021235 this_sequence A084483 A058509 A105109
Adjacent sequences: A020700 A020701 A020702 this_sequence A020704 A020705 A020706
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 02 2000
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