A059555 Beatty sequence for 1 + gamma A001620.

1, 3, 4, 6, 7, 9, 11, 12, 14, 15, 17, 18, 20, 22, 23, 25, 26, 28, 29, 31, 33, 34, 36, 37, 39, 41, 42, 44, 45, 47, 48, 50, 52, 53, 55, 56, 58, 59, 61, 63, 64, 66, 67, 69, 70, 72, 74, 75, 77, 78, 80, 82, 83, 85, 86, 88, 89, 91, 93, 94, 96, 97, 99, 100, 102, 104, 105, 107, 108

Offset: 1

Author

Mitch Harris, Jan 22 2001

Keywords

• nonn
• easy

Comments

Let r = gamma (the Euler constant, 0.5772...). When {k*r, k >= 1} is jointly ranked with the positive integers, A059555(n) is the position of n and A059556(n) is the position of n*r. - Clark Kimberling, Oct 21 2014

Links

• Harry J. Smith, Table of n, a(n) for n = 1..2000
• Fraenkel, Aviezri S.; Levitt, Jonathan; Shimshoni, Michael; Characterization of the set of values f(n)=[n alpha], n=1,2,..., Discrete Math. 2 (1972), no. 4, 335-345.
• Eric Weisstein's World of Mathematics, Beatty Sequence.
• Index entries for sequences related to Beatty sequences

Crossrefs

Beatty complement is A059556.

Programs

Magma

R:=RealField(100); [Floor((1+EulerGamma(R))*n): n in [1..100]]; // G. C. Greubel, Aug 27 2018

Maple

A001620 := proc(n)
        floor((1+gamma)*n) ;
end proc:
seq(A001620(n),n=1..50) ; # R. J. Mathar, Nov 11 2011

Mathematica

t = N[Table[k*EulerGamma, {k, 1, 200}]]; u = Union[Range[200], t]
Flatten[Table[Flatten[Position[u, n]], {n, 1, 100}]]  (* A059556 *)
Flatten[Table[Flatten[Position[u, t[[n]]]], {n, 1, 100}]] (* A059555 *)
(* Clark Kimberling, Oct 21 2014 *)

PARI

{ default(realprecision, 100); b=1 + Euler; for (n = 1, 2000, write("b059555.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 28 2009

Formula

a(n) = n + A038128(n).