# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a329993 Showing 1-1 of 1 %I A329993 #7 Jan 24 2020 11:10:47 %S A329993 1,3,5,6,8,10,11,13,15,16,18,20,21,23,25,26,28,30,32,33,35,37,38,40, %T A329993 42,43,45,47,48,50,52,53,55,57,58,60,62,64,65,67,69,70,72,74,75,77,79, %U A329993 80,82,84,85,87,89,91,92,94,96,97,99,101,102,104,106,107 %N A329993 Beatty sequence for x^2, where 1/x^2 + 1/2^x = 1. %C A329993 Let x be the solution of 1/x^2 + 1/2^x = 1. Then (floor(n x^2)) and (floor(n 2^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 A329993 Eric Weisstein's World of Mathematics, Beatty Sequence. %H A329993 Index entries for sequences related to Beatty sequences %F A329993 a(n) = floor(n*x^2), where x = 1.29819... is the constant in A329992; a(n) first differs from A064994(n) at n=89. %t A329993 r = x /. FindRoot[1/x^2 + 1/2^x == 1, {x, 1, 10}, WorkingPrecision -> 120] %t A329993 RealDigits[r][[1]] (* A329992 *) %t A329993 Table[Floor[n*r^2], {n, 1, 250}] (* A329993 *) %t A329993 Table[Floor[n*2^r], {n, 1, 250}] (* A329994 *) %Y A329993 Cf. A329825, A329992, A329994 (complement). %K A329993 nonn,easy %O A329993 1,2 %A A329993 _Clark Kimberling_, Jan 02 2020 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE