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A059555 Beatty sequence for 1 + gamma A001620. 4

%I

%S 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,

%T 41,42,44,45,47,48,50,52,53,55,56,58,59,61,63,64,66,67,69,70,72,74,75,

%U 77,78,80,82,83,85,86,88,89,91,93,94,96,97,99,100,102,104,105,107,108

%N Beatty sequence for 1 + gamma A001620.

%C 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

%H Harry J. Smith, <a href="/A059555/b059555.txt">Table of n, a(n) for n = 1..2000</a>

%H Fraenkel, Aviezri S.; Levitt, Jonathan; Shimshoni, Michael; <a href="http://dx.doi.org/10.1016/0012-365X(72)90012-X">Characterization of the set of values f(n)=[n alpha], n=1,2,...</a>, Discrete Math. 2 (1972), no. 4, 335-345.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence.</a>

%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>

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

%p A001620 := proc(n)

%p floor((1+gamma)*n) ;

%p end proc:

%p seq(A001620(n),n=1..50) ; # _R. J. Mathar_, Nov 11 2011

%t t = N[Table[k*EulerGamma, {k, 1, 200}]]; u = Union[Range[200], t]

%t Flatten[Table[Flatten[Position[u, n]], {n, 1, 100}]] (* A059556 *)

%t Flatten[Table[Flatten[Position[u, t[[n]]]], {n, 1, 100}]] (* A059555 *)

%t (* _Clark Kimberling_, Oct 21 2014 *)

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

%o (MAGMA) R:=RealField(100); [Floor((1+EulerGamma(R))*n): n in [1..100]]; // _G. C. Greubel_, Aug 27 2018

%Y Beatty complement is A059556.

%K nonn,easy

%O 1,2

%A _Mitch Harris_, Jan 22 2001

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Last modified July 23 21:10 EDT 2021. Contains 346265 sequences. (Running on oeis4.)