This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380099 #33 Apr 21 2025 10:44:40
%S A380099 4,97,888,9551,13549,505311,4601995,87956765,298132602
%N A380099 a(n) is the n-digit numerator of the fraction h/k with h and k coprime positive integers at which abs((h/k)^4-Pi) is minimal.
%C A380099 a(1)^4 = 4^4 = 256 corresponds to the numerator of A210621.
%C A380099 It appears that the number of correct decimal digits of Pi obtained from the fraction a(n)/A380100(n) is A130773(n-1) for n > 1 (see Spezia in Links). - _Stefano Spezia_, Apr 20 2025
%H A380099 Stefano Spezia, <a href="/A380099/a380099.pdf">Number of correct decimal digits of Pi obtained from (A380099(n)/A380100(n))^4 for n = 1..9</a>.
%H A380099 <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>.
%e A380099 n (h/k)^4 approximated value
%e A380099 - ------------------- ------------------
%e A380099 1 (4/3)^4 3.1604938271604...
%e A380099 2 (97/73)^4 3.1174212867620...
%e A380099 3 (888/667)^4 3.1415829223858...
%e A380099 4 (9551/7174)^4 3.1415927852873...
%e A380099 5 (13549/10177)^4 3.1415926560044...
%e A380099 ...
%t A380099 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, hmin]]; a
%Y A380099 Cf. A000796, A092040, A130773, A210621.
%Y A380099 Cf. A355622, A364844, A380100 (denominator).
%K A380099 nonn,base,frac,more
%O A380099 1,1
%A A380099 _Stefano Spezia_, Jan 12 2025
%E A380099 a(6)-a(9) from _Kritsada Moomuang_, Apr 17 2025