A309930 Decimal expansion of the constant whose continued fraction representation is the cubes [0; 1, 8, 27, 64, ...], A000578.

8, 8, 9, 3, 4, 4, 0, 0, 0, 0, 3, 2, 7, 6, 2, 6, 9, 3, 6, 0, 5, 4, 9, 4, 7, 0, 6, 3, 2, 1, 2, 2, 1, 9, 8, 1, 0, 3, 5, 4, 2, 9, 2, 0, 8, 8, 6, 3, 6, 8, 0, 9, 5, 4, 5, 4, 8, 8, 8, 0, 9, 1, 4, 4, 4, 3, 0, 9, 6, 7, 6, 4, 1, 7, 6, 8, 1, 4, 9, 8, 0, 5, 6, 1, 8, 3, 4

Offset: 0

Author

Daniel Hoyt, Nov 11 2019

Keywords

• cons
• nonn

Examples

			0.8893440000327626936054947063212219810354292088...
		

Crossrefs

Cf. A000578, A052119, A073824.

Programs

Mathematica

N[FromContinuedFraction[Table[k^3, {k, 0, 1000}]], 120] (* Vaclav Kotesovec, Nov 20 2019 *)

PARI

dec_exp(v)= w=contfracpnqn(v); w[1, 1]/w[2, 1]+0.
dec_exp(vector(2000, i, (i-1)^3)) \\ Michel Marcus, Nov 19 2019; after A073824

Python

import decimal
from decimal import Decimal as D
def constant_from_cofr(clist):
    hn0, kn0 = 0, 1
    hn1, kn1 = 1, 0
    for n in clist:
        hn2 = (n * hn1) + hn0
        kn2 = (n * kn1) + kn0
        hn0, kn0 = hn1, kn1
        hn1, kn1 = hn2, kn2
    return D(hn2)/D(kn2)
if _name_ == "_main_":
    prec = 200
    decimal.getcontext().prec = prec
    glist = [x**3 for x in range(500)]
    print(', '.join(str(x) for x in str(constant_from_cofr(glist))[2:]))