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

1, 2, 14, 45, 107, 138, 276, 414, 1135, 2270, 6672, 12209, 18881, 180865, 361730, 542595, 723460, 2031679, 7945851, 15891702, 21805874, 29751725, 43611748, 65417622, 87223496, 362754007, 384559881, 406365755

Offset: 1

Author

Benoit Cloitre and Paul D. Hanna, Jan 21 2003

Keywords

• nonn
• more
• changed

Comments

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.

Examples

			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.
		

Crossrefs

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

Extensions

a(15)-a(28) from Sean A. Irvine, Aug 30 2025