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 A083028 Numbers that are congruent to {0, 2, 3, 5, 7, 8, 11} mod 12. 16
 0, 2, 3, 5, 7, 8, 11, 12, 14, 15, 17, 19, 20, 23, 24, 26, 27, 29, 31, 32, 35, 36, 38, 39, 41, 43, 44, 47, 48, 50, 51, 53, 55, 56, 59, 60, 62, 63, 65, 67, 68, 71, 72, 74, 75, 77, 79, 80, 83, 84, 86, 87, 89, 91, 92, 95, 96, 98, 99, 101, 103, 104, 107, 108, 110, 111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The key-numbers of the pitches of a minor scale on a standard chromatic keyboard, with root = 0 and raised seventh. LINKS Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1). FORMULA G.f.: x^2*(x + 1)*(x^5 + 2*x^4 - x^3 + 3*x^2 - x + 2)/((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 19 2016: (Start) a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8. a(n) = (84*n - 84 - 9*(n mod 7) + 5*((n + 1) mod 7) - 2*((n + 2) mod 7) - 2*((n + 3) mod 7) + 5*((n + 4) mod 7) - 2*((n + 5) mod 7) + 5*((n + 6) mod 7))/49. a(7k) = 12k - 1, a(7k-1) = 12k - 4, a(7k-2) = 12k - 5, a(7k-3) = 12k - 7, a(7k - 4) = 12k - 9, 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 A083028:=n->12*floor(n/7)+[0, 2, 3, 5, 7, 8, 11][(n mod 7)+1]: seq(A083028(n), n=0..100); # Wesley Ivan Hurt, Jul 19 2016 MATHEMATICA Select[Range[0, 150], MemberQ[{0, 2, 3, 5, 7, 8, 11}, Mod[#, 12]] &] (* Wesley Ivan Hurt, Jul 19 2016 *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 2, 3, 5, 7, 8, 11, 12}, 70] (* Jianing Song, Sep 22 2018 *) PROG (MAGMA) [n : n in [0..150] | n mod 12 in [0, 2, 3, 5, 7, 8, 11]]; // Wesley Ivan Hurt, Jul 19 2016 (PARI) x='x+O('x^99); concat(0, Vec(x^2*(1+x)*(x^5+2*x^4-x^3+3*x^2-x+2)/((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): A083120 Dorian mode (D): A083033 Aeolian mode (A): A060107 (raised seventh: this sequence) Phrygian mode (E): A083034 Locrian mode (B): A082977 Chords: Major chord: A083030 Minor chord: A083031 Dominant seventh chord: A083032 Sequence in context: A189299 A028780 A284655 * A281015 A288625 A189168 Adjacent sequences:  A083025 A083026 A083027 * A083029 A083030 A083031 KEYWORD nonn,easy AUTHOR James Ingram (j.ingram(AT)t-online.de), Jun 01 2003 STATUS approved

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Last modified October 14 02:19 EDT 2019. Contains 327994 sequences. (Running on oeis4.)