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 A083026 Numbers that are congruent to {0, 2, 4, 5, 7, 9, 11} mod 12. 16
 0, 2, 4, 5, 7, 9, 11, 12, 14, 16, 17, 19, 21, 23, 24, 26, 28, 29, 31, 33, 35, 36, 38, 40, 41, 43, 45, 47, 48, 50, 52, 53, 55, 57, 59, 60, 62, 64, 65, 67, 69, 71, 72, 74, 76, 77, 79, 81, 83, 84, 86, 88, 89, 91, 93, 95, 96, 98, 100, 101, 103, 105, 107, 108, 110 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Key-numbers of the pitches of a major scale on a standard chromatic keyboard, with root = 0. Also key-numbers of the pitches of an Ionian mode scale on a standard chromatic keyboard, with root = 0. An Ionian mode scale can, for example, be played on consecutive white keys of a standard keyboard, starting on the root tone C. Cumulative sum of A291454. - Halfdan Skjerning, Aug 30 2017 LINKS G. C. Greubel, 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*(x + 1)*(x^5 + x^4 + x^3 + x^2 + 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 20 2016: (Start) a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8. a(n) = (84*n - 70 - 2*(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) + 5*((n + 6) mod 7))/49. a(7k) = 12k - 1, 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 A083026:=n->12*floor(n/7)+[0, 2, 4, 5, 7, 9, 11][(n mod 7)+1]: seq(A083026(n), n=0..100); # Wesley Ivan Hurt, Jul 20 2016 MATHEMATICA Select[Range[0, 150], MemberQ[{0, 2, 4, 5, 7, 9, 11}, Mod[#, 12]] &] (* Wesley Ivan Hurt, Jul 20 2016 *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 2, 4, 5, 7, 9, 11, 12}, 70] (* Jianing Song, Sep 22 2018 *) PROG (MAGMA) [n : n in [0..150] | n mod 12 in [0, 2, 4, 5, 7, 9, 11]]; // Wesley Ivan Hurt, Jul 20 2016 (PARI) a(n)=[-1, 0, 2, 4, 5, 7, 9][n%7+1] + n\7*12 \\ Charles R Greathouse IV, Jul 20 2016 (PARI) x='x+O('x^99); concat(0, Vec(x^2*(x+1)*(x^5+x^4+x^3+x^2+2)/((x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2))) \\ Jianing Song, Sep 22 2018 CROSSREFS Cf. A291454. A guide for some sequences related to modes and chords: Modes: Lydian mode (F): A083089 Ionian mode (C): this sequence Mixolydian mode (G): A083120 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: A114055 A169581 A184858 * A047379 A093848 A049039 Adjacent sequences:  A083023 A083024 A083025 * A083027 A083028 A083029 KEYWORD nonn,easy AUTHOR James Ingram (j.ingram(AT)t-online.de), Jun 01 2003 STATUS approved

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Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)