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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 November 21 09:14 EST 2019. Contains 329362 sequences. (Running on oeis4.)