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A309930
Decimal expansion of the constant whose continued fraction representation is the cubes [0; 1, 8, 27, 64, ...], A000578.
2
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
0,1
EXAMPLE
0.8893440000327626936054947063212219810354292088...
MATHEMATICA
N[FromContinuedFraction[Table[k^3, {k, 0, 1000}]], 120] (* Vaclav Kotesovec, Nov 20 2019 *)
PROG
(Python 3)
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:]))
(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
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Daniel Hoyt, Nov 11 2019
STATUS
approved