cp's OEIS Frontend

A083028 Numbers that are congruent to {0, 2, 3, 5, 7, 8, 11} mod 12.

%I A083028 #26 Sep 08 2022 08:45:10
%S A083028 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,
%T A083028 43,44,47,48,50,51,53,55,56,59,60,62,63,65,67,68,71,72,74,75,77,79,80,
%U A083028 83,84,86,87,89,91,92,95,96,98,99,101,103,104,107,108,110,111
%N A083028 Numbers that are congruent to {0, 2, 3, 5, 7, 8, 11} mod 12.
%C A083028 The key-numbers of the pitches of a minor scale on a standard chromatic keyboard, with root = 0 and raised seventh.
%H A083028 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F A083028 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
%F A083028 From _Wesley Ivan Hurt_, Jul 19 2016: (Start)
%F A083028 a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8.
%F A083028 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.
%F A083028 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)
%F A083028 a(n) = a(n-7) + 12 for n > 7. - _Jianing Song_, Sep 22 2018
%p A083028 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
%t A083028 Select[Range[0, 150], MemberQ[{0, 2, 3, 5, 7, 8, 11}, Mod[#, 12]] &] (* _Wesley Ivan Hurt_, Jul 19 2016 *)
%t A083028 LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 2, 3, 5, 7, 8, 11, 12}, 70] (* _Jianing Song_, Sep 22 2018 *)
%o A083028 (Magma) [n : n in [0..150] | n mod 12 in [0, 2, 3, 5, 7, 8, 11]]; // _Wesley Ivan Hurt_, Jul 19 2016
%o A083028 (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
%Y A083028 A guide for some sequences related to modes and chords:
%Y A083028 Modes:
%Y A083028 Lydian mode (F): A083089
%Y A083028 Ionian mode (C): A083026
%Y A083028 Mixolydian mode (G): A083120
%Y A083028 Dorian mode (D): A083033
%Y A083028 Aeolian mode (A): A060107 (raised seventh: this sequence)
%Y A083028 Phrygian mode (E): A083034
%Y A083028 Locrian mode (B): A082977
%Y A083028 Chords:
%Y A083028 Major chord: A083030
%Y A083028 Minor chord: A083031
%Y A083028 Dominant seventh chord: A083032
%K A083028 nonn,easy
%O A083028 1,2
%A A083028 James Ingram (j.ingram(AT)t-online.de), Jun 01 2003