A063705 -id:A063705

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page 1

A063706

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

+10
5

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

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

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

MATHEMATICA

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

CROSSREFS

Cf. A063705, A051258, A063704, A063708.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 03 2001

EXTENSIONS

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

STATUS

approved

A063703

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

+10
4

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

Index entries for cyclotomic polynomials, values at phi

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 *)

CROSSREFS

Cf. A019320, A063705, A063707, A063704.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 03 2001

EXTENSIONS

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

STATUS

approved

A063707

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

+10
4

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

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

Index entries for cyclotomic polynomials, values at phi

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

MATHEMATICA

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

CROSSREFS

Cf. A019320, A063703, A063705, A063708.