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 A060107 Numbers that are congruent to {0, 2, 3, 5, 7, 8, 10} mod 12. The ivory keys on a piano, start with A0 = the 0th key. 19
 0, 2, 3, 5, 7, 8, 10, 12, 14, 15, 17, 19, 20, 22, 24, 26, 27, 29, 31, 32, 34, 36, 38, 39, 41, 43, 44, 46, 48, 50, 51, 53, 55, 56, 58, 60, 62, 63, 65, 67, 68, 70, 72, 74, 75, 77, 79, 80, 82, 84, 86, 87, 89, 91, 92, 94, 96, 98, 99, 101, 103, 104, 106, 108, 110, 111, 113, 115 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS More precisely, the key-numbers of the pitches of a minor scale on a standard chromatic keyboard, with root = 0 and flat seventh. Also key-numbers of the pitches of an Aeolian mode scale on a standard chromatic keyboard, with root = 0. An Aeolian mode scale can, for example, be played on consecutive white keys of a standard keyboard, starting on the root tone A. A piano sequence since if a(n) < 88 then A059620(a(n)) = 0. 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 a(n) = a(n-7) + 12 for n > 7. a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8. G.f.: x^2*(2 + x + 2*x^2 + 2*x^3 + x^4 + 2*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) = (84*n - 91 - 2*(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) - 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 - 10, a(7k-6) = 12k - 12. (End) a(n) = A081031(n) - 1 for 1 <= n <= 36. - Jianing Song, Oct 14 2019 MAPLE A060107:=n->12*floor(n/7)+[0, 2, 3, 5, 7, 8, 10][(n mod 7)+1]: seq(A060107(n), n=0..100); # Wesley Ivan Hurt, Jul 20 2016 MATHEMATICA Select[Range[0, 120], MemberQ[{0, 2, 3, 5, 7, 8, 10}, Mod[#, 12]]&] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 2, 3, 5, 7, 8, 10, 12}, 70] (* Harvey P. Dale, Nov 10 2011 *) PROG (MAGMA) [n : n in [0..150] | n mod 12 in [0, 2, 3, 5, 7, 8, 10]]; // Wesley Ivan Hurt, Jul 20 2016 (PARI) x='x+O('x^99); concat(0, Vec(x^2*(2+x+2*x^2+2*x^3+x^4+2*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 Cf. A059620, A081031. Complement of A060106. 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): this sequence (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: A001912 A186221 A083027 * A333230 A159556 A219643 Adjacent sequences:  A060104 A060105 A060106 * A060108 A060109 A060110 KEYWORD easy,nonn AUTHOR Henry Bottomley, Feb 27 2001 STATUS approved

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Last modified September 20 19:48 EDT 2020. Contains 337265 sequences. (Running on oeis4.)