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Least k such that tan(k) > tan(a(n-1)), for n >= 1, where a(0) = 0.
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%I #35 Jul 02 2019 10:00:57

%S 0,1,14,36,58,80,102,124,146,168,190,212,234,256,278,300,322,344,699,

%T 1054,1409,1764,2119,2474,2829,3184,3539,3894,4249,4604,4959,5314,

%U 5669,6024,6379,6734,7089,7444,7799,8154,8509,8864,9219,9574,9929,10284,10639,10994,11349

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

%C 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

%H Michel Marcus, <a href="/A024814/b024814.txt">Table of n, a(n) for n = 0..177</a> (terms 0..175 from I. V. Serov)

%t 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 *)

%o (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

%Y Cf. A000503, A024815, A024818.

%K nonn

%O 0,3

%A _Clark Kimberling_