A063705 -id:A063705 - cp's OEIS frontend

A063706 Cyclotomic polynomials Phi_n at x=phi, divided by sqrt(5) and rounded to nearest integer (where phi = tau = (sqrt(5)+1)/2).

1, 0, 1, 2, 2, 7, 1, 20, 4, 10, 2, 143, 2, 376, 5, 12, 21, 2583, 7, 6764, 15, 75, 34, 46367, 18, 7435, 89, 2618, 104, 832039, 25, 2178308, 987, 3400, 610, 20161, 136, 39088168, 1597, 23229, 861, 267914295, 182, 701408732, 4895, 35921, 10946, 4807526975

Offset: 0

Antti Karttunen, Aug 03 2001

nonn

Paolo Xausa, Table of n, a(n) for n = 0..1000

Cf. A063705, A051258, A063704, A063708.

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))/(sqrt(5)))),j=0..120)];

Join[{1}, Round[Simplify[Cyclotomic[Range[50], GoldenRatio]]/Sqrt[5]]] (* Paolo Xausa, Feb 27 2024 *)

a(43) and a(47) corrected by Sean A. Irvine, May 08 2023

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

Antti Karttunen, Aug 03 2001

nonn

Cf. A019320, A063705, A063707, A063704.

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)];

Floor[Simplify[Cyclotomic[Range[0, 50],GoldenRatio]]] (* Paolo Xausa, Feb 27 2024 *)

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

A063707 Cyclotomic polynomials Phi_n at x=phi, ceiled up (where phi = tau = (sqrt(5)+1)/2).

Original entry on oeis.org

2, 1, 3, 6, 4, 17, 2, 46, 8, 24, 5, 321, 6, 842, 12, 26, 48, 5777, 15, 15126, 35, 167, 77, 103681, 42, 16627, 200, 5856, 234, 1860497, 57, 4870846, 2208, 7602, 1365, 45081, 306, 87403802, 3572, 51941, 1927, 599074577, 408, 1568397606, 10947, 80321

Offset: 0

Antti Karttunen, Aug 03 2001

nonn

Cf. A019320, A063703, A063705, A063708.

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)))),j=0..120)];

Join[{2}, Ceiling[Simplify[Cyclotomic[Range[50], GoldenRatio]]]] (* Paolo Xausa, Feb 27 2024 *)

cp's OEIS Frontend

A063706 Cyclotomic polynomials Phi_n at x=phi, divided by sqrt(5) and rounded to nearest integer (where phi = tau = (sqrt(5)+1)/2).

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

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Extensions

A063707 Cyclotomic polynomials Phi_n at x=phi, ceiled up (where phi = tau = (sqrt(5)+1)/2).

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Crossrefs

Programs

Maple

Mathematica