OFFSET
1,1
COMMENTS
In music theory the repeating sequence '2,2,1,2,2,2,1' is the number of steps of half tones in pitch between the tones of a major scale. Starting at, for example, the tone 'C' that is the first tone of the C major scale, 2 half tones up leads to 'D', which is the second tone in the scale. The scale then is: C,D,E,F,G,A,B and C. Starting at another term in the sequence will produce a different scale; for example, '2,1,2,2,1,2,2' will produce a minor scale.
From Robert G. Wilson v, Aug 25 2017: (Start)
First forward difference of A083026.
Decimal expansion of 737407/3333333. (End)
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..1000
Wikipedia, Scale (music)
FORMULA
a(n) = floor(12*(n+1)/7) - floor(12*n/7). - Federico Provvedi, Oct 18 2018
Dirichlet g.f.: 2*zeta(s) - 7^(-s)*(zeta(s,3/7) + zeta(s)). - Federico Provvedi, Aug 27 2021
MAPLE
a:=proc(n) floor(12*(n+1)/7-floor(12*n/7)) end: seq(a(n), n=1..110); # Muniru A Asiru, Oct 19 2018
MATHEMATICA
Table[{2, 2, 1, 2, 2, 2, 1}, 15] // Flatten (* Robert G. Wilson v, Aug 25 2017 *)
Table[Floor[12/7 (k + 1)] - Floor[12/7 k], {k, 1, 100}] (* Federico Provvedi, Oct 18 2018 *)
PROG
(PARI) a(n)=[1, 2, 2, 1, 2, 2, 2][n%7+1] \\ Charles R Greathouse IV, Aug 26 2017
(Magma) [12*(n+1) div 7 - 12*n div 7: n in [1..80]]; // Vincenzo Librandi, Oct 21 2018
CROSSREFS
KEYWORD
AUTHOR
Halfdan Skjerning, Aug 24 2017
STATUS
approved