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A004739
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Concatenation of sequences (1,2,2,..,n-1,n-1,n,n,n-1,n-1,..,2,2,1) for n >= 1.
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3
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1, 1, 1, 2, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Also called Smarandache Crescendo Symmetric Sequence.
Contribution from Artur Jasinski (grafix(AT)csl.pl), Mar 07 2010: (Start)
Zeta[2,k/p]+Zeta[2,(p-k)/p]=(Pi/Sin[(Pi*a(n))/p])2, where p=2,3,4, k=1..p-1.
This sequence is odd subset of A003983 for odd p=3,5,7,9,....
For even subset of A003983 see A004737 (End)
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REFERENCES
| F. Smarandache, "Collected Papers", Vol. II, Tempus Publ. Hse., Bucharest, 1996; F. Smarandache, "Numerical Sequences", University of Craiova, 1975; [ See Arizona State University, Special Collection, Tempe, AZ, USA ].
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems, Hexis, Phoenix, 2006.
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LINKS
| M. L. Perez et al., eds., Smarandache Notions Journal
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
F. Smarandache, Collected Papers, Vol. II
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
| See Mathematica code. [From Artur Jasinski (grafix(AT)csl.pl), Mar 07 2010]
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MATHEMATICA
| aa = {}; Do[Do[AppendTo[aa, (p/Pi) ArcSin[Sqrt[1/((1/Pi^2) (Zeta[2, k/p] + Zeta[2, (p - k)/p]))]]], {k, 1, p - 1}], {p, 3, 50, 2}]; Round[N[aa, 50]] (*Artur Jasinski*) [From Artur Jasinski (grafix(AT)csl.pl), Mar 07 2010]
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PROG
| (Haskell)
a004739 n = a004739_list !! (n-1)
a004739_list = concat $ map (\n -> [1..n] ++ [n, n-1..1]) [1..]
-- Reinhard Zumkeller, Mar 26 2011
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CROSSREFS
| Cf. A004737, A004738, A004731.
A003983, A004737. [From Artur Jasinski (grafix(AT)csl.pl), Mar 07 2010]
Sequence in context: A025863 A136605 A165621 * A156282 A203776 A120423
Adjacent sequences: A004736 A004737 A004738 * A004740 A004741 A004742
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KEYWORD
| nonn,easy
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AUTHOR
| R. Muller
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EXTENSIONS
| More terms from Patrick De Geest (pdg(AT)worldofnumbers.com), Jun 15 1998.
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