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 A083034 Numbers that are congruent to {0, 1, 3, 5, 7, 8, 10} mod 12. 15
 0, 1, 3, 5, 7, 8, 10, 12, 13, 15, 17, 19, 20, 22, 24, 25, 27, 29, 31, 32, 34, 36, 37, 39, 41, 43, 44, 46, 48, 49, 51, 53, 55, 56, 58, 60, 61, 63, 65, 67, 68, 70, 72, 73, 75, 77, 79, 80, 82, 84, 85, 87, 89, 91, 92, 94, 96, 97, 99, 101, 103, 104, 106, 108, 109, 111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Key-numbers of the pitches of a Phrygian mode scale on a standard chromatic keyboard, with root = 0. A Phrygian mode scale can, for example, be played on consecutive white keys of a standard keyboard, starting on the root tone E. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..2000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1). FORMULA G.f.: x^2*(x + 1)*(2*x^5 + x^3 + x^2 + x + 1)/((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 - 98 - 2*(n mod 7) + 5*((n + 1) mod 7) - 2*((n + 2) mod 7) - 2*((n + 3) mod 7) - 2*((n + 4) mod 7) + 5*((n + 5) mod 7) - 2*((n + 6) mod 7))/49. a(7k) = 12k - 2, a(7k-1) = 12k - 4, a(7k-2) = 12k - 5, a(7k-3) = 12k - 7, a(7k-4) = 12k - 9, a(7k-5) = 12k - 11, a(7k-6) = 12k - 12. (End) a(n) = a(n-7) + 12 for n > 7. - Jianing Song, Sep 22 2018 MAPLE A083034:=n->12*floor(n/7)+[0, 1, 3, 5, 7, 8, 10][(n mod 7)+1]: seq(A083034(n), n=0..100); # Wesley Ivan Hurt, Jul 20 2016 MATHEMATICA Select[Range[0, 150], MemberQ[{0, 1, 3, 5, 7, 8, 10}, Mod[#, 12]] &] (* Wesley Ivan Hurt, Jul 20 2016 *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 5, 7, 8, 10, 12}, 70] (* Jianing Song, Sep 22 2018 *) PROG (MAGMA) [n : n in [0..150] | n mod 12 in [0, 1, 3, 5, 7, 8, 10]]; // Wesley Ivan Hurt, Jul 20 2016 (PARI) x='x+O('x^99); concat(0, Vec(x^2*(x+1)*(2*x^5+x^3+x^2+x+1)/((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: A083028) Phrygian mode (E): this sequence Locrian mode (B): A082977 Chords: Major chord: A083030 Minor chord: A083031 Dominant seventh chord: A083032 Sequence in context: A285074 A186219 A185050 * A213908 A247514 A144077 Adjacent sequences:  A083031 A083032 A083033 * A083035 A083036 A083037 KEYWORD nonn,easy AUTHOR James Ingram (j.ingram(AT)t-online.de), Jun 01 2003 STATUS approved

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Last modified December 6 07:00 EST 2019. Contains 329784 sequences. (Running on oeis4.)