cp's OEIS Frontend

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.

Showing 1-2 of 2 results.

A022789 Place where n-th 1 occurs in A023127.

Original entry on oeis.org

1, 4, 9, 17, 27, 40, 55, 73, 93, 116, 141, 168, 198, 230, 265, 302, 342, 384, 429, 476, 525, 577, 631, 688, 747, 809, 873, 940, 1009, 1081, 1155, 1231, 1310, 1391, 1475, 1561, 1650, 1741, 1835, 1931, 2029, 2130, 2233, 2339, 2447, 2558, 2671, 2787
Offset: 1

Views

Author

Clark Kimberling

Keywords

Extensions

Missing 2339 inserted by Sean A. Irvine, May 21 2019

A258054 Circle of fifths cycle (counterclockwise).

Original entry on oeis.org

1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8
Offset: 1

Views

Author

Peter Woodward, May 17 2015

Keywords

Comments

The twelve notes dividing the octave are numbered 1 through 12 sequentially. This sequence begins at a certain note, travels down a perfect fifth twelve times (seven semitones), and arrives back at the same note. If justly tuned fifths are used, the final note will be flat by the Pythagorean comma (roughly 23.46 cents or about a quarter of a semitone).
Period 12: repeat [1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8]. - Omar E. Pol, May 18 2015
The string [1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8] is also in both A023127 and A054073. - Omar E. Pol, May 19 2015

Examples

			For a(3), 1+5+5 = 11 (mod 12).
For a(4), 1+5+5+5 = 4 (mod 12).

Links

Crossrefs

Cf. A221363 (Pythagorean comma), A257811 (clockwise circle of fifths cycle).

Programs

  • Magma
    [1+5*(n-1) mod 12: n in [1..80]]; // Vincenzo Librandi, May 19 2015
  • Maple
    A258054:=n->1+(5*(n-1) mod 12): seq(A258054(n), n=1..100); # Wesley Ivan Hurt, May 22 2015
  • Mathematica
    PadRight[{}, 100, {1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8}] (* Vincenzo Librandi, May 19 2015 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},{1, 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8},108] (* Ray Chandler, Aug 27 2015 *)
  • PARI
    a(n)=1+5*(n-1) \\ Charles R Greathouse IV, May 22 2015
  • PARI
    Vec(x*(1 + 6*x + 11*x^2 + 4*x^3 + 9*x^4 + 2*x^5 + 7*x^6 + 12*x^7 + 5*x^8 + 10*x^9 + 3*x^10 + 8*x^11) / (1 - x^12) + O(x^80)) \\ Colin Barker, Nov 15 2019

Formula

Periodic with period 12: a(n) = 1 + (5(n-1) mod 12).
From Colin Barker, Nov 15 2019: (Start)
G.f.: x*(1 + 6*x + 11*x^2 + 4*x^3 + 9*x^4 + 2*x^5 + 7*x^6 + 12*x^7 + 5*x^8 + 10*x^9 + 3*x^10 + 8*x^11) / (1 - x^12).
a(n) = a(n-12) for n>12.
(End)

Extensions

Extended by Ray Chandler, Aug 27 2015
Showing 1-2 of 2 results.

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