A392558 - OEIS

A392558

Decimal expansion of the number whose continued fraction coefficients are given in A390946.

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

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OFFSET

0,1

COMMENTS

The constant is normal in the continued fraction sense since its continued fraction coefficients follow the Gauss-Kuzmin distribution by construction.

LINKS

Jwalin Bhatt, Table of n, a(n) for n = 0..10000

FORMULA

Equals lim_{n->oo} A391906(n) / A391907(n).

EXAMPLE

0.707523727401943349910145193792719566756305655575218020444...

PROG

(Python) # Using sample_gauss_kuzmin_distribution function from A390946.

from sympy import floor, prime, Rational, continued_fraction_iterator, continued_fraction_convergents

from collections import deque

from os.path import commonprefix

def reliable_digits_from_cf(coeffs, prec):

frac_lower, frac_upper = deque(continued_fraction_convergents(coeffs+[1]), maxlen=2)

trunc_lower, trunc_upper = floor(frac_lower * 10**prec), floor(frac_upper * 10**prec)

return commonprefix([str(trunc_lower), str(trunc_upper)])

coeffs = [0] + [cf for i in range(2, 12) for j in range(1, i) for cf in continued_fraction_iterator(Rational(prime(i), prime(j)))]

num = reliable_digits_from_cf(coeffs, prec=200)

A392558 = [int(d) for d in num]

CROSSREFS

Cf. A390946 (continued fraction), A391906, A391907.

Sequence in context: A085966 A010678 A010503 * A335727 A381979 A158857

Adjacent sequences: A392555 A392556 A392557 * A392559 A392560 A392561

KEYWORD

nonn,cons

AUTHOR

Jwalin Bhatt, Jan 16 2026

STATUS

approved