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

Author

Clark Kimberling

Keywords

• nonn

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)

Crossrefs

Cf. A000503, A024815, A024818.

Programs

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 *)

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