A330064 - OEIS

%I #4 Jan 04 2020 12:57:31

%S 2,5,7,10,13,15,18,20,23,26,28,31,34,36,39,41,44,47,49,52,55,57,60,62,

%T 65,68,70,73,75,78,81,83,86,89,91,94,96,99,102,104,107,110,112,115,

%U 117,120,123,125,128,130,133,136,138,141,144,146,149,151,154,157

%N Beatty sequence for cosh(x), where 1/x + sech(x) = 1.

%C Let x be the solution of 1/x + sech(x) = 1. Then (floor(n x) and (floor(n cosh(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 x), where x = x = 1.61749989... is the constant in A330062.

%t r = x /. FindRoot[1/x + 1/Cosh[x] == 1, {x, 2, 10}, WorkingPrecision -> 210]

%t RealDigits[r][[1]] (* A330062 *)

%t Table[Floor[n*r], {n, 1, 250}]        (* A330063 *)

%t Table[Floor[n*Cosh[r]], {n, 1, 250}]  (* A330064 *)

%Y Cf. A329825, A330062, A330063 (complement).

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jan 04 2020