A372869 - OEIS

%I #59 Dec 26 2024 13:28:36

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

%T 2,4,7,7,6,3,0,5,6,6,9,6,2,0,0,9,2,3,0,1,3,6,2,1,2,1,5,5,5,1,5,7,6,7,

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

%N Decimal expansion of the number whose continued fraction coefficients are given in A084580.

%e 0.5815803358828329856145006072280655247763056696200923013621215551576710...

%o (Python) # Using `sample_gauss_kuzmin_distribution` function from A084580.

%o from mpmath import mp, iv

%o def decimal_from_cf(coeffs):

%o     num = iv.mpf([coeffs[-1], coeffs[-1]+1])

%o     for coeff in coeffs[-2::-1]:

%o         num = coeff + 1/iv.mpf(num)

%o     return 1/num

%o def get_matching_digits(interval_a, interval_b):

%o     match_index = 0

%o     for i, j in zip(interval_a, interval_b):

%o         if i != j:  break

%o         match_index += 1

%o     return interval_a[:match_index]

%o def compute_kuzmin_digits(prec, num_coeffs):

%o     assert prec > num_coeffs

%o     mp.dps = iv.dps = prec

%o     coeffs = sample_gauss_kuzmin_distribution(num_coeffs)

%o     x = decimal_from_cf(coeffs)

%o     a = mp.nstr(mp.mpf(x.a), n=prec, strip_zeros=False)

%o     b = mp.nstr(mp.mpf(x.b), n=prec, strip_zeros=False)

%o     return get_matching_digits(a, b)

%o num = compute_kuzmin_digits(prec=200, num_coeffs=180)

%o A372869 = [int(d) for d in num[1:] if d != '.']

%Y Cf. A084580 (continued fraction).

%K cons,nonn

%O 0,1

%A _Jwalin Bhatt_, Jul 04 2024