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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. 5
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.

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)

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

CROSSREFS

Complement of A060106. A piano sequence since if a(n)<88 then A059620(a(n))=0.

Sequence in context: A001912 A186221 A083027 * A159556 A219643 A194798

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 January 18 18:32 EST 2018. Contains 297864 sequences.