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Search: id:A038722
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| A038722 |
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Take the sequence of natural numbers (A000027) and reverse successive subsequences of lengths 1,2,3,4,... |
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+0
8
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| 1, 3, 2, 6, 5, 4, 10, 9, 8, 7, 15, 14, 13, 12, 11, 21, 20, 19, 18, 17, 16, 28, 27, 26, 25, 24, 23, 22, 36, 35, 34, 33, 32, 31, 30, 29, 45, 44, 43, 42, 41, 40, 39, 38, 37, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 78, 77, 76
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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The rectangular array having A038722 as antidiagonals is the transpose of the rectangular array given by A000217. Column 1 of array A038722 is A000124 (central polygonal numbers). Array A038722 is the dispersion of the complement of A000124. - Clark Kimberling (ck6(AT)evansville.edu), Apr 05 2003
a(n) is the smallest number not yet in the sequence such that n + a(n) is one more than a square. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 06 2009]
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REFERENCES
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Suggested by correspondence with Michael Somos.
R. Honsberger, "Ingenuity in Mathematics", Table 10.4 on page 87.
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LINKS
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Index entries for sequences that are permutations of the natural numbers
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FORMULA
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a(n) =[sqrt(2n-1)-1/2]*[sqrt(2n-1)+3/2]-n+2 =A061579(n-1)+1. Seen as a square table by antidiagonals, T(n, k)=k+(n+k-1)*(n+k-2)/2, i.e. the transpose of A000027 as a square table.
G.f.: g(x)=x/(1-x)*(psi(x)-x/(1-x)+2*sum{k>=0, k*x^(k*(k+1)/2)}) where psi(x)=sum{k>=0, x^(k*(k+1)/2)}=1/2*x^(-1/8)*theta_2(0,x^(1/2) is a Ramanujan theta function. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 08 2007
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CROSSREFS
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A self-inverse permutation of the natural numbers.
Cf. A000027, A020703.
Sequence in context: A058401 A105027 A120913 this_sequence A145522 A131968 A132665
Adjacent sequences: A038719 A038720 A038721 this_sequence A038723 A038724 A038725
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KEYWORD
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nonn,tabl
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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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