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 1-3 of 3 results.

A063708 Cyclotomic polynomials Phi_n at x=phi divided by sqrt(5) and ceiled up (where phi = tau = (sqrt(5)+1)/2).

Original entry on oeis.org

1, 1, 2, 3, 2, 8, 1, 21, 4, 11, 3, 144, 3, 377, 6, 12, 22, 2584, 7, 6765, 16, 75, 35, 46368, 19, 7436, 90, 2619, 105, 832040, 26, 2178309, 988, 3400, 611, 20161, 137, 39088169, 1598, 23229, 862, 267914296, 183, 701408733, 4896, 35921, 10947, 4807526976
Offset: 0

Views

Author

Antti Karttunen, Aug 03 2001

Keywords

Links

Crossrefs

Cf. A063707, A051258, A063704, A063706.

Programs

  • Maple
    with(numtheory); Phi_at_x := (n,y) -> subs(x=y,cyclotomic(n,x)); [seq(ceil(evalf(simplify(Phi_at_x(j,(sqrt(5)+1)/2))/(sqrt(5)))),j=0..120)];
  • Mathematica
    Ceiling[Simplify[Cyclotomic[Range[0, 50], GoldenRatio]]/Sqrt[5]] (* Paolo Xausa, Feb 27 2024 *)

A063703 Cyclotomic polynomials Phi_n at x=phi, floored down (where phi = tau = (sqrt(5)+1)/2).

Original entry on oeis.org

1, 0, 2, 5, 3, 16, 2, 45, 7, 23, 4, 320, 5, 841, 11, 25, 47, 5776, 14, 15125, 34, 166, 76, 103680, 41, 16626, 199, 5855, 233, 1860496, 56, 4870845, 2207, 7601, 1364, 45080, 305, 87403801, 3571, 51940, 1926, 599074576, 407, 1568397605, 10946, 80320
Offset: 0

Views

Author

Antti Karttunen, Aug 03 2001

Keywords

Links

Crossrefs

Cf. A019320, A063705, A063707, A063704.

Programs

  • Maple
    with(numtheory); Phi_at_x := (n,y) -> subs(x=y,cyclotomic(n,x)); [seq(floor(evalf(simplify(Phi_at_x(j,(sqrt(5)+1)/2)))),j=0..120)];
  • Mathematica
    Floor[Simplify[Cyclotomic[Range[0, 50],GoldenRatio]]] (* Paolo Xausa, Feb 27 2024 *)

Extensions

a(43) corrected by Sean A. Irvine, May 08 2023

A063705 Cyclotomic polynomials Phi_n at x=phi, rounded to nearest integer (where phi = tau = (sqrt(5)+1)/2).

Original entry on oeis.org

2, 1, 3, 5, 4, 16, 2, 45, 8, 23, 5, 320, 5, 841, 11, 26, 48, 5776, 15, 15125, 34, 167, 76, 103680, 41, 16626, 199, 5855, 233, 1860496, 56, 4870845, 2208, 7602, 1364, 45081, 305, 87403801, 3571, 51941, 1926, 599074576, 407, 1568397605, 10946, 80321
Offset: 0

Views

Author

Antti Karttunen, Aug 03 2001

Keywords

Links

Crossrefs

Cf. A019320, A063703, A063707, A063706.

Programs

  • Maple
    with(numtheory); Phi_at_x := (n,y) -> subs(x=y,cyclotomic(n,x)); [seq(round(evalf(simplify(Phi_at_x(j,(sqrt(5)+1)/2)))),j=0..120)];
  • Mathematica
    Join[{2}, Round[Simplify[Cyclotomic[Range[50], GoldenRatio]]]] (* Paolo Xausa, Feb 27 2024 *)

Extensions

a(43) corrected by Sean A. Irvine, May 08 2023
Showing 1-3 of 3 results.

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