A327788 a(n) is the smallest nonnegative integer m such that the integer part of tan(m) is equal to n.

0, 1, 20, 17, 105, 237, 303, 14, 58, 80, 124, 146, 11151, 168, 46318, 190, 46695, 212, 23997, 58432, 234, 13014, 38574, 61649, 82949, 256, 16586, 33271, 48891, 63091, 76581, 89361, 278, 8088, 18738, 28678, 37908, 46783, 54948, 63113, 70568, 77668, 84768, 91158, 97193, 300, 4915, 10240, 15565, 20535, 25150

Offset

0,3

Links

Rémy Sigrist, Table of n, a(n) for n = 0..5000

Example

tan(0) = 0, so a(0) = 0.
tan(1) = 1.557407724654902230506974807... so a(1) = 1.
For m = 2, 3, 4, ... , 13, 15, 16, 18, 19, tan(m) < 2, tan (14) = 7.24460661609480..., tan(17) = 3.493915645474... and tan(20) = 2.2371609442247422652871732477... so a(2) = 20.

Mathematica

Array[Block[{m = 0}, While[IntegerPart@ Tan@ m != #, m++]; m] &, 40, 0] (* Michael De Vlieger, Oct 05 2019 *)

Prog

(Python) import numpy as np
import math as m
n = 1
i = 0
inp = np.zeros(1)
out = inp
while n < 10001:
    k=m.trunc(m.tan(i))
    if k==n:
        inp = np.append(inp, int(n))
        out = np.append(out, int(i))
        print(n, i)
        n += 1
        i = 0
        continue
    else:
        i+=1
(Magma) a:=[]; for n in [0..50] do m:=0; while Floor(Tan(m)) ne n do m:=m+1; end while; Append(~a, m); end for; a; // Marius A. Burtea, Oct 05 2019
(PARI) a(n) = my(k=0); while (floor(tan(k)) != n, k++); k; \\ Michel Marcus, Oct 05 2019

Crossrefs

Cf. A000503 (floor(tan(n))).

Sequence in context: A040382 A223283 A375787 * A376974 A365065 A076119

Adjacent sequences: A327785 A327786 A327787 * A327789 A327790 A327791

Keyword

nonn,look,easy

Author

James Carruthers, Sep 25 2019

Status

approved