A024814 Least k such that tan(k) > tan(a(n-1)), for n >= 1, where a(0) = 0.

0, 1, 14, 36, 58, 80, 102, 124, 146, 168, 190, 212, 234, 256, 278, 300, 322, 344, 699, 1054, 1409, 1764, 2119, 2474, 2829, 3184, 3539, 3894, 4249, 4604, 4959, 5314, 5669, 6024, 6379, 6734, 7089, 7444, 7799, 8154, 8509, 8864, 9219, 9574, 9929, 10284, 10639, 10994, 11349

Offset

0,3

Comments

The difference between a(n) and a(n+1) is 22 for a(2) through a(16). Then the difference between a(n) and a(n+1) is 355 for a(17) through a(162). Then it appears that the difference is 104348 for at least some terms beginning with a(163) but computing subsequent terms of the sequence is very slow so it is not easy to know whether or for how long that 104358 difference persists. - Harvey P. Dale, Jun 29 2019

Links

Michel Marcus, Table of n, a(n) for n = 0..177 (terms 0..175 from I. V. Serov)

Mathematica

lk[n_]:=Module[{k=n+1, t=Tan[n]}, While[Tan[k]<=t, k++]; k]; NestList[lk, 0, 50] (* Harvey P. Dale, Jun 29 2019 *)

Prog

(PARI) lista(nn) = {last = 0; lastk = 0; print1(lastk, ", "); for (i=1, nn, k = lastk; while (tan(k) <= last, k++; ); print1(k, ", "); last = tan(k); lastk = k; ); } \\ Michel Marcus, Mar 23 2013

Crossrefs

Cf. A000503, A024815, A024818.

Sequence in context: A115664 A182753 A263124 * A340460 A268319 A177722

Adjacent sequences: A024811 A024812 A024813 * A024815 A024816 A024817

Keyword

nonn

Author

Clark Kimberling

Status

approved