A062389 a(n) = floor( (2n-1)*Pi/2 ).

1, 4, 7, 10, 14, 17, 20, 23, 26, 29, 32, 36, 39, 42, 45, 48, 51, 54, 58, 61, 64, 67, 70, 73, 76, 80, 83, 86, 89, 92, 95, 98, 102, 105, 108, 111, 114, 117, 120, 124, 127, 130, 133, 136, 139, 142, 146, 149, 152, 155, 158, 161, 164, 168, 171, 174, 177, 180, 183, 186

Offset: 1

Author

Jason Earls, Jul 08 2001

Keywords

• nonn
• easy

Comments

In general, the complement of a nonhomogenous Beatty sequence [n*r + h] is given by [n*s + h - h*s], where s = r/(r - 1). As an example, the complement of this sequence is A246046. This sequence gives the positive integers k satisfying tan(k) > tan(k + 1), and A246046 gives those satisfying tan(k) < tan(k + 1). - Clark Kimberling, Aug 24 2014

Excluding a(1), a(n) = positive floored solutions to tan(x) = x. - Derek Orr, May 30 2015

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 223.

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A246046.

Programs

Maple

seq(floor((2*n-1)*Pi/2), n=1..1000); # Robert Israel, Jun 01 2015

Mathematica

r = Pi; s = Pi/(Pi - 1); h = -Pi/2; z = 120;
u = Table[Floor[n*r + h], {n, 1, z}] (* A062389 *)
v = Table[Floor[n*s + h - h*s], {n, 1, z}]  (* A246046 *)
(* Clark Kimberling, Aug 24 2014 *)

PARI

j=[]; for(n=1,150,j=concat(j,floor(1/2*(2*n-1)*Pi))); j

PARI

{ default(realprecision, 50); for (n=1, 1000, write("b062389.txt", n, " ", (2*n - 1)*Pi\2); ) } \\ Harry J. Smith, Aug 06 2009