A380100 a(n) is the denominator of the fraction h/k with h and k coprime positive integers at which abs((h/k)^4-Pi) is minimal, with the numerator h of n digits.

3, 73, 667, 7174, 10177, 379552, 3456676, 66066573, 223935013

Offset: 1

Author

Stefano Spezia, Jan 12 2025

Keywords

• nonn
• base
• frac
• more

Comments

a(1)^4 = 3^4 = 81 corresponds to the denominator of A210621.

It appears that the number of correct decimal digits of Pi obtained from the fraction A380099(n)/a(n) is A130773(n-1) for n > 1 (see Spezia in Links). - Stefano Spezia, Apr 20 2025

Examples

			  n               (h/k)^4    approximated value
  -   -------------------    ------------------
  1               (4/3)^4    3.1604938271604...
  2             (97/73)^4    3.1174212867620...
  3           (888/667)^4    3.1415829223858...
  4         (9551/7174)^4    3.1415927852873...
  5       (13549/10177)^4    3.1415926560044...
  ...
		

Links

• Stefano Spezia, Number of correct decimal digits of Pi obtained from (A380099(n)/A380100(n))^4 for n = 1..9.
• Index entries for sequences related to the number Pi.

Crossrefs

Cf. A000583, A000796, A130773, A210621.

Cf. A355623, A364845, A380099 (numerator).

Programs

Mathematica

nmax = 3; a = {}; hmin = kmin = 0; For[n = 1, n <= nmax, n++, minim = Infinity; For[h = 10^(n-1), h <10^n, h++, For[k = 1, k < 10^n/Pi^(1/4), k++, If[(dist = Abs[h^4/k^4-Pi]) < minim && GCD[h,k]==1, minim = dist; hmin=h; kmin = k]]]; AppendTo[a, kmin]]; a

Extensions

a(6)-a(9) from Kritsada Moomuang, Apr 17 2025