A119953 Y = X = 'i + .25(ii + jj + kk + e); Z = 'i - i' + .5(jj + kk - jk + kj) + e. See pdf-file for an exact definition (this sequence gives an initial term 1); Version "jes".

1, 1, 4, 2, 1, 6, 7, 4, 2, 6, 6, 1, 2, 4, 7, 1, 2, 4, -1, -3, 0, 4, -1, -11, -6, -1, -5, -13, -10, -4, -10, -14, -10, -9, -13, -17, -12, -11, -19, -18, -13, -15, -19, -18, -15, -18, -23, -19, -15, -18, -25, -23, -18, -22, -30, -25, -20, -27, -34, -30, -24, -30, -39, -35, -26, -33, -44, -39, -31, -35, -46, -42, -34, -39, -47

Offset: 0

Author

Creighton Dement, May 30 2006

Keywords

• sign
• hear

Comments

Compare with A108618. Beginning at a(16350) = 560, the sequence apparently enters a loop and repeats the 60 terms: 560, 382, 327, 503, 558, 383, 328, 503, 557, 383, 327, 504, 558, 382, 327, 504, 560, 381, 327, 506, 559, 380, 327, 507, 559, 377, 326, 508, 558, 377, 328, 508, 559, 377, 326, 509, 560, 377, 325, 509, 559, 378, 326, 508, 559, 378, 328, 507, 559, 380, 327, 506, 559, 381, 327, 503, 558, 382, 326, 503.

Let f(n) give the frequency of occurrence of the number n in the above 60 term set. Then f(560) = 3, f(382) = 3, f(327) = 7, f(503) = 4, f(558) = 4, f(383) = 2, f(328) = 3, f(557) = 1, f(504) = 2, f(381) = 2, f(506) = 2, f(559) = 7, f(380) = 2, f(507) = 2, f(377) = 4, f(326) = 4, f(508) = 3, f(509) = 2, f(325) = 1, f(378) = 2

Example MUSICALGORITHMS settings (link): Pitch: Scale values 11-66, Duration: Scaling 0-2 (perform division operation).

Links

• Creighton Dement, Table of n, a(n) for n = 0..30000
• Creighton Dement, Construction of an integer sequence with musical properties
• J. Middleton, Musicalgorithms.

Crossrefs

Cf. A119954, A108618.