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A060107
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Numbers that are congruent to {0, 2, 3, 5, 7, 8, 10} mod 12. The ivory keys on a piano.
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4
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..68.
Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).
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FORMULA
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a(n)=a(n-7)+12 .
a(n)= +a(n-1) +a(n-7) -a(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
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MATHEMATICA
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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] (* From Harvey P. Dale, Nov 10 2011 *)
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CROSSREFS
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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
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley, Feb 27 2001
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STATUS
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approved
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