This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A257811 #49 Aug 18 2023 23:52:05
%S A257811 1,8,3,10,5,12,7,2,9,4,11,6,1,8,3,10,5,12,7,2,9,4,11,6,1,8,3,10,5,12,
%T A257811 7,2,9,4,11,6,1,8,3,10,5,12,7,2,9,4,11,6,1,8,3,10,5,12,7,2,9,4,11,6,1,
%U A257811 8,3,10,5,12,7,2,9,4,11,6,1,8,3,10,5,12,7,2,9,4,11,6,1,8,3,10,5,12,7,2,9,4,11,6,1,8,3,10,5,12,7,2,9,4,11,6
%N A257811 Circle of fifths cycle (clockwise).
%C A257811 The twelve notes dividing the octave are numbered 1 through 12 sequentially. This sequence begins at a certain note, travels up a perfect fifth (seven semitones) twelve times, and arrives back at the same note. If justly tuned fifths are used, the final note will be sharp by the Pythagorean comma (roughly 23.46 cents or about a quarter of a semitone).
%C A257811 Period 12: repeat [1, 8, 3, 10, 5, 12, 7, 2, 9, 4, 11, 6]. - _Omar E. Pol_, May 12 2015
%H A257811 Alonso del Arte, Alvin Hoover Belt, Daniel Forgues, and Charles R Greathouse IV, <a href="https://oeis.org/wiki/The_multi-faceted_reach_of_the_OEIS#Music">The multi-faceted reach of the OEIS: Music</a>
%H A257811 Wikipedia, <a href="http://en.wikipedia.org/wiki/Circle_of_fifths">Circle of fifths</a>
%H A257811 Wikipedia, <a href="http://en.wikipedia.org/wiki/Pythagorean_comma">Pythagorean comma</a>
%H A257811 <a href="https://oeis.org/index/Mu#music">OEIS index entry for music</a>
%H A257811 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,1).
%F A257811 Periodic with period 12: a(n) = 1 + 7*(n-1) mod 12.
%F A257811 From _Colin Barker_, Nov 15 2019: (Start)
%F A257811 G.f.: x*(1 + 8*x + 3*x^2 + 10*x^3 + 5*x^4 + 12*x^5 + 7*x^6 + 2*x^7 + 9*x^8 + 4*x^9 + 11*x^10 + 6*x^11) / (1 - x^12).
%F A257811 a(n) = a(n-12) for n > 12.
%F A257811 (End)
%e A257811 For a(3), 1+7+7 == 3 (mod 12).
%e A257811 For a(4), 1+7+7+7 == 10 (mod 12).
%t A257811 PadRight[{}, 100, {1, 8, 3, 10, 5, 12, 7, 2, 9, 4, 11, 6}] (* _Vincenzo Librandi_, May 10 2015 *)
%t A257811 LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},{1, 8, 3, 10, 5, 12, 7, 2, 9, 4, 11, 6},108] (* _Ray Chandler_, Aug 27 2015 *)
%o A257811 (Magma) [1+7*(n-1) mod(12): n in [1..80]]; // _Vincenzo Librandi_, May 10 2015
%o A257811 (PARI) a(n)=7*(n-1)%12+1 \\ _Charles R Greathouse IV_, Jun 02 2015
%o A257811 (PARI) Vec(x*(1 + 8*x + 3*x^2 + 10*x^3 + 5*x^4 + 12*x^5 + 7*x^6 + 2*x^7 + 9*x^8 + 4*x^9 + 11*x^10 + 6*x^11) / (1 - x^12) + O(x^80)) \\ _Colin Barker_, Nov 15 2019
%Y A257811 Cf. A194835 (Contains this circle of fifths sequence), A007337 (sqrt(3) sequence), A258054 (counterclockwise circle of fifths cycle).
%K A257811 nonn,easy
%O A257811 1,2
%A A257811 _Peter Woodward_, May 09 2015
%E A257811 Extended by _Ray Chandler_, Aug 27 2015