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 A083120 Numbers that are congruent to {0, 2, 4, 5, 7, 9, 10} mod 12. 15
 0, 2, 4, 5, 7, 9, 10, 12, 14, 16, 17, 19, 21, 22, 24, 26, 28, 29, 31, 33, 34, 36, 38, 40, 41, 43, 45, 46, 48, 50, 52, 53, 55, 57, 58, 60, 62, 64, 65, 67, 69, 70, 72, 74, 76, 77, 79, 81, 82, 84, 86, 88, 89, 91, 93, 94, 96, 98, 100, 101, 103, 105, 106, 108, 110 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Key-numbers of the pitches of a Mixolydian mode scale on a standard chromatic keyboard, with root = 0. A Mixolydian mode scale can, for example, be played on consecutive white keys of a standard keyboard, starting on the root tone G. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1). FORMULA G.f.: x^2*(2 + 2*x + x^2 + 2*x^3 + 2*x^4 + x^5 + 2*x^6)/((x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x - 1)^2). - R. J. Mathar, Oct 08 2011 From Wesley Ivan Hurt, Jul 20 2016: (Start) a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8. a(n) = (84*n - 77 + 5*(n mod 7) - 2*((n + 1) mod 7) - 2*((n + 2) mod 7) + 5*((n + 3) mod 7) - 2*((n + 4) mod 7) - 2*((n + 5) mod 7) - 2*((n + 6) mod 7))/49. a(7k) = 12k - 2, a(7k-1) = 12k - 3, a(7k-2) = 12k - 5, a(7k-3) = 12k - 7, a(7k-4) = 12k - 8, a(7k-5) = 12k - 10, a(7k-6) = 12k - 12. (End) a(n) = a(n-7) + 12 for n > 7. - Jianing Song, Sep 22 2018 MAPLE A083120:=n->12*floor(n/7)+[0, 2, 4, 5, 7, 9, 10][(n mod 7)+1]: seq(A083120(n), n=0..100); # Wesley Ivan Hurt, Jul 20 2016 MATHEMATICA Select[Range[0, 120], MemberQ[{0, 2, 4, 5, 7, 9, 10}, Mod[#, 12]]&] (* Harvey P. Dale, Feb 20 2011 *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 2, 4, 5, 7, 9, 10, 12}, 70] (* Jianing Song, Sep 22 2018 *) PROG (MAGMA) [n : n in [0..150] | n mod 12 in [0, 2, 4, 5, 7, 9, 10]]; // Wesley Ivan Hurt, Jul 20 2016 (PARI) a(n)=[-2, 0, 2, 4, 5, 7, 9][n%7+1] + n\7*12 \\ Charles R Greathouse IV, Jul 21 2016 (PARI) x='x+O('x^99); concat(0, Vec(x^2*(2+2*x+x^2+2*x^3+2*x^4+x^5+2*x^6)/((x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2))) \\ Jianing Song, Sep 22 2018 CROSSREFS A guide for some sequences related to modes and chords: Modes: Lydian mode (F): A083089 Ionian mode (C): A083026 Mixolydian mode (G): this sequence Dorian mode (D): A083033 Aeolian mode (A): A060107 (raised seventh: A083028) Phrygian mode (E): A083034 Locrian mode (B): A082977 Chords: Major chord: A083030 Minor chord: A083031 Dominant seventh chord: A083032 Sequence in context: A106829 A190228 A286667 * A001614 A284535 A244222 Adjacent sequences:  A083117 A083118 A083119 * A083121 A083122 A083123 KEYWORD nonn,easy AUTHOR James Ingram (j.ingram(AT)t-online.de), Jun 01 2003 STATUS approved

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Last modified September 20 20:02 EDT 2020. Contains 337265 sequences. (Running on oeis4.)