A096464
Let p(k)/q(k) = A096456(k)/A096463(k) be the k-th convergent to Pi/2; sequence gives numbers n such that |tan(p(n))|/p(n) sets a new maximal record.
Original entry on oeis.org
1, 4, 118, 136, 315, 3727, 3763, 15503, 153396, 156559, 984404, 1119377
Offset: 1
The fifth term is 315. This means that at p(315), which is a number near 2.37*10^154, |tan(p(315))|/p(315) sets a new record, a number near 556.31.
A096456
Numerators of convergents to Pi/2.
Original entry on oeis.org
1, 2, 3, 11, 344, 355, 51819, 52174, 260515, 573204, 4846147, 5419351, 37362253, 42781604, 122925461, 411557987, 534483448, 2549491779, 3083975227, 17969367914, 21053343141, 881156436695, 902209779836, 2685575996367
Offset: 1
1, 2, 3/2, 11/7, 344/219, 355/226, ...
- M. F. Hasler, Table of n, a(n) for n = 1..1500, Oct 13 2020
- I. Rosenholtz, Tangent sequences, world records, ..., Math. Mag., 72 (No. 5, 1999), 367-376.
Cf.
A002485 (numerators of convergents to Pi).
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Table[Numerator[FromContinuedFraction[ContinuedFraction[Pi/2, n]]], {n, 1, 25}] (* Stefan Steinerberger, Mar 18 2006 *)
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contfracpnqn(c=contfrac(Pi/2),#c)[1,] \\ M. F. Hasler, Oct 13 2020
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