A330115 - OEIS

%I #10 Dec 19 2024 06:16:56

%S 3,6,9,12,16,19,22,25,28,32,35,38,41,45,48,51,54,57,61,64,67,70,73,77,

%T 80,83,86,90,93,96,99,102,106,109,112,115,118,122,125,128,131,135,138,

%U 141,144,147,151,154,157,160,163,167,170,173,176,180,183,186

%N Beatty sequence for e^x, where 1/e^x + csch(x) = 1.

%C Let x be the positive solution of 1/e^x + csch(x) = 1. Then (floor(n*e^x)) and (floor(n*sinh(x))) are a pair of Beatty sequences; i.e., every positive integer is in exactly one of the sequences. See the Guide to related sequences at A329825.

%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) = floor(n*e^x), where x = 1.1676157... is the constant in A330114.

%t r = x /. FindRoot[1/E^x + Csch[x] == 1, {x, 1, 2}, WorkingPrecision -> 200]

%t RealDigits[r][[1]] (* A330114 *)

%t Table[Floor[n*E^r], {n, 1, 250}]  (* A330115 *)

%t Table[Floor[n*Sinh[r]], {n, 1, 250}]  (* A330116 *)

%Y Cf. A329825, A330114, A330116 (complement).

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jan 04 2020