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Search: id:A099957
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| A099957 |
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a(n) = Sum_{i=0..n-1} phi(2i+1). |
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+0
5
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| 1, 3, 7, 13, 19, 29, 41, 49, 65, 83, 95, 117, 137, 155, 183, 213, 233, 257, 293, 317, 357, 399, 423, 469, 511, 543, 595, 635, 671, 729, 789, 825, 873, 939, 983, 1053, 1125, 1165, 1225, 1303, 1357, 1439, 1503, 1559, 1647, 1719, 1779, 1851, 1947
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The n-th term is the number of notes of the (2n-1)-limit tonality diamond. This is a term from music theory, and means the scale consisting of the rational numbers r, 1 <= r < 2, such that the odd part of both the numerator and the denominator of r, when reduced to lowest terms, is less than or equal to the fixed odd number 2n-1. - Gene Ward Smith (genewardsmith(AT)gmail.com), Mar 27 2006
(1/4)*Number of distinct angular positions under which an observer positioned at the center of a square of a square lattice can see the (2n) X (2n) points symmetrically surrounding his position.
(1/8)*number of distinct angular positions under which an observer positioned at a lattice point of a square lattice can see the (2n+1)X(2n+1) points symmetrically surrounding his position gives A002088.
(1/2)*number of distinct angular positions under which an observer positioned at the center of an edge of a square lattice can see the (2n)X(2n-1) points symmetrically surrounding his position gives A099958.
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LINKS
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Wikipedia, Tonality diamond
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FORMULA
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a(n+1)-a(n)=phi(2n+1) (A037225).
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CROSSREFS
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Cf. A000010, A002088, A099958, A049687.
Sequence in context: A100458 A000960 A031215 this_sequence A086148 A007645 A015916
Adjacent sequences: A099954 A099955 A099956 this_sequence A099958 A099959 A099960
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Nov 13 2004
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