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 A171372 a(n) = Numerator of 1/(2*n)^2 - 1/(3*n)^2 for n > 0, a(0) = 1. 1
 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The diagonal of a table of numerators of the Rydberg-Ritz spectrum of hydrogen:   1,  1,  1,   1,  1,   1,  1,   1,  1,   1,   1, ... A000012   0,  5,  3,  21,  2,  45, 15,  77,  6, 117,  35, ... A061037   0,  9,  5,  33,  3,  65, 21, 105,  1, 153,  45, ... A061041   0, 13,  7,   5,  4,  85,  1, 133, 10,   7,  55, ... A061045   0, 17,  9,  57,  5, 105, 33, 161,  3, 225,  65, ... A061049   0, 21, 11,  69,  6,   1, 39, 189, 14, 261,   3, ...   0, 25, 13,   1,  7, 145,  5, 217,  1,  11,  85, ...   0, 29, 15,  93,  8, 165, 51,   5, 18, 333,  95, ...   0, 33, 17, 105,  9, 185, 57, 273,  5, 369, 105, ...   0, 37, 19,  13, 10, 205,  7, 301, 22,   5, 115, ...   0, 41, 21, 129, 11,   9, 69, 329,  3, 441,   1, ... In that respect, constructed similar to A144437. LINKS FORMULA a(n) = numerator of 5/(6*n)^2 . Period 5: repeat [1,5,5,5,5]. G.f.: (1 + 5*x + 5*x^2 + 5*x^3 + 5*x^4)/((1-x)*(1 + x + x^2 + x^3 + x^4)). a(n) = 4*(n^4 mod 5)+1, with n >= 0. - Paolo P. Lava, Dec 14 2009 a(n) = 1 + 4*sign(n mod 5). - Wesley Ivan Hurt, Sep 26 2018 a(n) = (21-8*cos(2*n*Pi/5)-8*cos(4*n*Pi/5))/5. - Wesley Ivan Hurt, Sep 27 2018 MATHEMATICA Table[If[n==0, 1, Numerator[5/(6*n)^2]], {n, 0, 100}] (* G. C. Greubel, Sep 20 2018 *) PROG (PARI) concat([1], vector(100, n, numerator(5/(6*n)^2))) \\ G. C. Greubel, Sep 20 2018 (MAGMA) [1] cat [Numerator(5/(6*n)^2): n in [1..100]]; // G. C. Greubel, Sep 20 2018 CROSSREFS Cf. A171373 (binomial transform), A171408, A105371. Sequence in context: A232614 A254609 A133707 * A083945 A125563 A093704 Adjacent sequences:  A171369 A171370 A171371 * A171373 A171374 A171375 KEYWORD nonn,easy,frac AUTHOR Paul Curtz, Dec 07 2009 EXTENSIONS Edited by R. J. Mathar, Dec 15 2009 STATUS approved

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Last modified August 17 12:30 EDT 2022. Contains 356189 sequences. (Running on oeis4.)