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A079937 Greedy frac multiples of Pi^2/6: a(1)=1, Sum_{n>=1} frac(a(n)*x) = 1 at x = Pi^2/6. 5

%I #14 Apr 11 2021 01:52:45

%S 1,2,14,45,107,138,276,414,1135,2270,6672,12209,18881,180865

%N Greedy frac multiples of Pi^2/6: a(1)=1, Sum_{n>=1} frac(a(n)*x) = 1 at x = Pi^2/6.

%C The n-th greedy frac multiple of x is the smallest integer that does not cause Sum_{k=1..n} frac(a(k)*x) to exceed unity; an infinite number of terms appear as the denominators of the convergents to the continued fraction of x.

%e a(4) = 45 since frac(1*x) + frac(2*x) + frac(14*x) + frac(45*x) < 1, while frac(1*x) + frac(2*x) + frac(14*x) + frac(k*x) > 1 for all k > 14 and k < 45.

%Y Cf. A080017 (denominators of convergents to Pi^2/6), A079934, A079938, A079939.

%K nonn,more

%O 1,2

%A _Benoit Cloitre_ and _Paul D. Hanna_, Jan 21 2003

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)