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%I #7 Jun 01 2022 18:10:44
%S 1,2,4,5,6,8,9,10,12,13,14,16,17,18,20,21,22,24,25,26,28,29,31,32,33,
%T 35,36,37,39,40,41,43,44,45,47,48,49,51,52,53,55,56,58,59,60,62,63,64,
%U 66,67
%N Beatty sequence for log x, where 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. A236229, A329825, A329977 (complement).
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jan 02 2020
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