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Search: id:A061038
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| A061038 |
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Denominator of 1/4 - 1/n^2. |
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+0
19
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| 1, 36, 16, 100, 9, 196, 64, 324, 25, 484, 144, 676, 49, 900, 256, 1156, 81, 1444, 400, 1764, 121, 2116, 576, 2500, 169, 2916, 784, 3364, 225, 3844, 1024, 4356, 289, 4900, 1296, 5476, 361, 6084, 1600, 6724, 441, 7396, 1936, 8100, 529, 8836
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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a(4n)=(2n+1)^2=A016754, a(2n+1)=(4n+2)^2, n pos=A016826(n+1), a(4n+2)=(4n)^2, n pos=A016802(n+1). J. J. Balmer, Notiz uber die Spectrallinien des Wasserstoffs, Annalen der Physik (und Chemie) 25,(1885),80-85. First text of two that year. Communicated June 25 1884 to the Naturforschende Gesellschaft in Basel (where Euler was born). [From Paul Curtz (bpcrtz(AT)free.fr), Oct 31 2008]
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LINKS
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Harry J. Smith, Table of n, a(n) for n=2,...,1000
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FORMULA
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a(4n+2) = (2n+1)^2, a(2n+3) = (4n+6)^2, a(4n+4) = (4n+4)^2. - Ralf Stephan, Jun 10 2005
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MATHEMATICA
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Table[Denominator[1/4 - 1/n^2], {n, 2, 60}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 08 2006
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PROGRAM
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(PARI) { for (n=2, 1000, write("b061038.txt", n, " ", denominator(1/4 - 1/n^2)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 17 2009]
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CROSSREFS
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See A061037 for comments, references, links.
Cf. A126252.
Sequence in context: A066583 A073405 A056770 this_sequence A058231 A008894 A033973
Adjacent sequences: A061035 A061036 A061037 this_sequence A061039 A061040 A061041
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KEYWORD
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nonn,frac,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 26 2001
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 08 2006
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