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A372869 Decimal expansion of the number whose continued fraction coefficients are given in A084580.

%I A372869 #59 Dec 26 2024 13:28:36
%S A372869 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 A372869 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 A372869 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 A372869 Decimal expansion of the number whose continued fraction coefficients are given in A084580.
%e A372869 0.5815803358828329856145006072280655247763056696200923013621215551576710...
%o A372869 (Python) # Using `sample_gauss_kuzmin_distribution` function from A084580.
%o A372869 from mpmath import mp, iv
%o A372869 def decimal_from_cf(coeffs):
%o A372869     num = iv.mpf([coeffs[-1], coeffs[-1]+1])
%o A372869     for coeff in coeffs[-2::-1]:
%o A372869         num = coeff + 1/iv.mpf(num)
%o A372869     return 1/num
%o A372869 def get_matching_digits(interval_a, interval_b):
%o A372869     match_index = 0
%o A372869     for i, j in zip(interval_a, interval_b):
%o A372869         if i != j:  break
%o A372869         match_index += 1
%o A372869     return interval_a[:match_index]
%o A372869 def compute_kuzmin_digits(prec, num_coeffs):
%o A372869     assert prec > num_coeffs
%o A372869     mp.dps = iv.dps = prec
%o A372869     coeffs = sample_gauss_kuzmin_distribution(num_coeffs)
%o A372869     x = decimal_from_cf(coeffs)
%o A372869     a = mp.nstr(mp.mpf(x.a), n=prec, strip_zeros=False)
%o A372869     b = mp.nstr(mp.mpf(x.b), n=prec, strip_zeros=False)
%o A372869     return get_matching_digits(a, b)
%o A372869 num = compute_kuzmin_digits(prec=200, num_coeffs=180)
%o A372869 A372869 = [int(d) for d in num[1:] if d != '.']
%Y A372869 Cf. A084580 (continued fraction).
%K A372869 cons,nonn
%O A372869 0,1
%A A372869 _Jwalin Bhatt_, Jul 04 2024