A329997 - OEIS

%I #13 Jul 12 2020 10:51:28

%S 3,6,10,13,17,20,24,27,30,34,37,41,44,48,51,54,58,61,65,68,72,75,78,

%T 82,85,89,92,96,99,102,106,109,113,116,120,123,126,130,133,137,140,

%U 144,147,150,154,157,161,164,168,171,174,178,181,185,188,192,195,198

%N Beatty sequence for 3^x, where 1/x^3 + 1/3^x = 1.

%C Let x be the solution of 1/x^3 + 1/3^x = 1. Then (floor(n*x^3)) and (floor(n*3^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*3^x), where x = 1.12177497... is the constant in A329995.

%t r = x /. FindRoot[1/x^3 + 1/3^x == 1, {x, 1, 10}, WorkingPrecision -> 120]

%t RealDigits[r][[1]] (* A329995 *)

%t Table[Floor[n*r^3], {n, 1, 250}]  (* A329996 *)

%t Table[Floor[n*3^r], {n, 1, 250}]  (* A329997 *)

%Y Cf. A329825, A329995, A329996 (complement).

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jan 03 2020