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A059556 Beatty sequence for 1 + 1/gamma.

%I A059556 #22 Feb 16 2025 08:32:44
%S A059556 2,5,8,10,13,16,19,21,24,27,30,32,35,38,40,43,46,49,51,54,57,60,62,65,
%T A059556 68,71,73,76,79,81,84,87,90,92,95,98,101,103,106,109,112,114,117,120,
%U A059556 122,125,128,131,133,136,139,142,144,147,150,153,155,158,161,163,166
%N A059556 Beatty sequence for 1 + 1/gamma.
%C A059556 Differs from A054088 at indices 56, 71, 112, 127, 142, 168, 183 etc. - _R. J. Mathar_, Oct 05 2008
%C A059556 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 A059556 Harry J. Smith, <a href="/A059556/b059556.txt">Table of n, a(n) for n = 1..2000</a>
%H A059556 Aviezri S. Fraenkel, Jonathan Levitt, Michael Shimshoni, <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 A059556 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence.</a>
%H A059556 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%t A059556 t = N[Table[k*EulerGamma, {k, 1, 200}]]; u = Union[Range[200], t]
%t A059556 Flatten[Table[Flatten[Position[u, n]], {n, 1, 100}]]  (* A059556 *)
%t A059556 Flatten[Table[Flatten[Position[u, t[[n]]]], {n, 1, 100}]] (* A059555 *)
%t A059556 (* _Clark Kimberling_, Oct 21 2014 *)
%o A059556 (PARI) { default(realprecision, 100); b=1 + 1/Euler; for (n = 1, 2000, write("b059556.txt", n, " ", floor(n*b)); ) } \\ _Harry J. Smith_, Jun 28 2009
%Y A059556 Beatty complement is A059555.
%K A059556 nonn,easy
%O A059556 1,1
%A A059556 _Mitch Harris_, Jan 22 2001