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Beatty sequence for the number x satisfying 1/x + 1/(log x) = 1.
3

%I #4 Jan 03 2020 20:19:42

%S 3,7,11,15,19,23,27,30,34,38,42,46,50,54,57,61,65,69,73,77,81,84,88,

%T 92,96,100,104,108,111,115,119,123,127,131,135,138,142,146,150,154,

%U 158,162,165,169,173,177,181,185,189,192

%N Beatty sequence for the number x satisfying 1/x + 1/(log x) = 1.

%C Let x be the real solution of 1/x + 1/(log x) = 1. Then (floor(n x)) and (floor(n*(log(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 = 3.8573348... is the constant in A236229.

%t r = x /. FindRoot[1/x + 1/Log[x] == 1, {x, 3, 4}, WorkingPrecision -> 210];

%t RealDigits[r][[1]]; (* A236229 *)

%t Table[Floor[n*r], {n, 1, 50}]; (* A329977 *)

%t Table[Floor[n*Log[r]], {n, 1, 50}]; (* A329978 *)

%Y Cf. A329825, A236229, A329978 (complement).

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jan 02 2020