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%I #18 Mar 16 2021 01:25:15
%S 1,4,11,22,80,355,11270,26087,286602,301419,5419351,21390802,
%T 144316263,167004362,2549491779,2816733503,5900708730,8984683957,
%U 30038027098,31037086001,84380376926,199507230388,302095980547,306607554715
%N Numbers k where the fractional part of tan(k) decreases monotonically to 0.
%e From _Jon E. Schoenfield_, Mar 16 2021: (Start)
%e "Fractional part" of x here is defined as x - floor(x), so, e.g., since tan(11) = -225.95084..., its fractional part is -225.95084... - (-226) = 0.04915...
%e Terms and fractional parts are as follows:
%e .
%e n k = a(n) tan(k) - floor(tan(k))
%e -- ------------ ----------------------
%e 1 1 0.55740772465490223...
%e 2 4 0.15782128234957758...
%e 3 11 0.04915354580485797...
%e 4 22 0.00885165604168446...
%e 5 80 0.00365494560707973...
%e 6 355 0.00003014435337318...
%e 7 11270 0.00001427816936167...
%e 8 26087 0.00000550749362596...
%e 9 286602 0.00000029389002962...
%e 10 301419 0.00000022540911069...
%e 11 5419351 0.00000003820047507...
%e 12 21390802 0.00000001171381405...
%e 13 144316263 0.00000000559574875...
%e 14 167004362 0.00000000046598564...
%e 15 2549491779 0.00000000044744949...
%e 16 2816733503 0.00000000037258234...
%e 17 5900708730 0.00000000022284805...
%e 18 8984683957 0.00000000007311376...
%e 19 30038027098 0.00000000006960700...
%e 20 31037086001 0.00000000001573866...
%e 21 84380376926 0.00000000001010671...
%e 22 199507230388 0.00000000000293624...
%e 23 302095980547 0.00000000000151187...
%e 24 306607554715 0.00000000000103988...
%e (End)
%o (PARI) lista(nn) = {my(m = oo, nm); for (n=1, nn, if ((nm=frac(tan(n))) < m, print1(n, ", "); m = nm););} \\ _Michel Marcus_, Jan 17 2019
%Y Cf. A019435 (increases).
%K nonn
%O 1,2
%A _Michel ten Voorde_
%E Offset changed to 1 and more terms from _Sean A. Irvine_, Jan 16 2019