The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A082977 Numbers that are congruent to {0, 1, 3, 5, 6, 8, 10} mod 12. 18
 0, 1, 3, 5, 6, 8, 10, 12, 13, 15, 17, 18, 20, 22, 24, 25, 27, 29, 30, 32, 34, 36, 37, 39, 41, 42, 44, 46, 48, 49, 51, 53, 54, 56, 58, 60, 61, 63, 65, 66, 68, 70, 72, 73, 75, 77, 78, 80, 82, 84, 85, 87, 89, 90, 92, 94, 96, 97, 99, 101, 102, 104, 106, 108, 109, 111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS James Ingram suggests that this (with the initial 0 omitted) is the correct version of Fludd's sequence, rather than A047329. See also A083026. Key-numbers of the pitches of a Hypophrygian mode scale on a standard chromatic keyboard, with root = 0. A Hypophrygian mode scale can, for example, be played on consecutive white keys of a standard keyboard, starting on the root tone B. - James Ingram (j.ingram(AT)t-online.de), Jun 01 2003 REFERENCES Robert Fludd, Utriusque Cosmi ... Historia, Oppenheim, 1617-1619. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Robert Fludd, Page 158 of "Utriusque Cosmi" in Beinecke Rare Book and Manuscript Library Photonegatives Collection. Robert Fludd, Larger version of the same image Robert Fludd, Utriusque Cosmi, Maioris scilicet et Minoris, metaphysica, physica, atque technica Historia, available as ZIP or PDF download. Wikipedia, Robert Fludd Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1). FORMULA G.f.: x*(1 + x + 2*x^4)*(1 + x + x^2)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - R. J. Mathar, Sep 17 2008 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 - 105 - 2*(n mod 7) - 2*((n + 1) mod 7) + 5*((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 - 6, 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 a(n) = floor(12*(n-1)/7). - Federico Provvedi, Oct 18 2018 MAPLE A082977:=n->12*floor(n/7)+[0, 1, 3, 5, 6, 8, 10][(n mod 7)+1]: seq(A082977(n), n=0..100); # Wesley Ivan Hurt, Jul 19 2016 MATHEMATICA CoefficientList[Series[x(1 + x + 2*x^4)(1 + x + x^2)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)), {x, 0, 100}], x] (* Vincenzo Librandi, Jan 06 2013 *) fQ[n_] := MemberQ[{0, 1, 3, 5, 6, 8, 10}, Mod[n, 12]]; Select[ Range[0, 111], fQ] (* Robert G. Wilson v, Jan 07 2014 *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 5, 6, 8, 10, 12}, 70] (* Jianing Song, Sep 22 2018 *) Floor@Range[0, 2^8, 12/7] (* Federico Provvedi, Oct 18 2018 *) PROG (Haskell) a082977 n = a082977_list !! (n-1) a082977_list = [0, 1, 3, 5, 6, 8, 10] ++ map (+ 12) a082977_list -- Reinhard Zumkeller, Jan 07 2014 (MAGMA) [n : n in [0..150] | n mod 12 in [0, 1, 3, 5, 6, 8, 10]]; // Wesley Ivan Hurt, Jul 19 2016 (PARI) x='x+O('x^99); concat(0, Vec(x*(1+x+2*x^4)*(1+x+x^2)/((1-x)^2*(1+x+x^2+x^3+x^4+x^5+x^6)))) \\ Jianing Song, Sep 22 2018 CROSSREFS Cf. A047329. Different from A000210. 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): A083034 Locrian mode (B): this sequence Chords: Major chord: A083030 Minor chord: A083031 Dominant seventh chord: A083032 Sequence in context: A299233 A320997 A083042 * A000210 A329829 A182760 Adjacent sequences:  A082974 A082975 A082976 * A082978 A082979 A082980 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, May 31 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 17 18:14 EST 2020. Contains 332005 sequences. (Running on oeis4.)