A016274 - OEIS

A016274

Numbers k where the fractional part of tan(k) decreases monotonically to 0.

1, 4, 11, 22, 80, 355, 11270, 26087, 286602, 301419, 5419351, 21390802, 144316263, 167004362, 2549491779, 2816733503, 5900708730, 8984683957, 30038027098, 31037086001, 84380376926, 199507230388, 302095980547, 306607554715 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	LINKS	`Table of n, a(n) for n=1..24.`
	EXAMPLE	`From Jon E. Schoenfield, Mar 16 2021: (Start)` `"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...` `Terms and fractional parts are as follows:` `.` `n k = a(n) tan(k) - floor(tan(k))` `-- ------------ ----------------------` `1 1 0.55740772465490223...` `2 4 0.15782128234957758...` `3 11 0.04915354580485797...` `4 22 0.00885165604168446...` `5 80 0.00365494560707973...` `6 355 0.00003014435337318...` `7 11270 0.00001427816936167...` `8 26087 0.00000550749362596...` `9 286602 0.00000029389002962...` `10 301419 0.00000022540911069...` `11 5419351 0.00000003820047507...` `12 21390802 0.00000001171381405...` `13 144316263 0.00000000559574875...` `14 167004362 0.00000000046598564...` `15 2549491779 0.00000000044744949...` `16 2816733503 0.00000000037258234...` `17 5900708730 0.00000000022284805...` `18 8984683957 0.00000000007311376...` `19 30038027098 0.00000000006960700...` `20 31037086001 0.00000000001573866...` `21 84380376926 0.00000000001010671...` `22 199507230388 0.00000000000293624...` `23 302095980547 0.00000000000151187...` `24 306607554715 0.00000000000103988...` `(End)`
	PROG	`(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`
	CROSSREFS	`Cf. A019435 (increases).` `Sequence in context: A259574 A008249 A174405 * A092656 A269743 A298790` `Adjacent sequences: A016271 A016272 A016273 * A016275 A016276 A016277`
	KEYWORD	`nonn`
	AUTHOR	`Michel ten Voorde`
	EXTENSIONS	`Offset changed to 1 and more terms from Sean A. Irvine, Jan 16 2019`
	STATUS	`approved`