

A330002


Beatty sequence for x, where 1/x + 1/(x+1)^2 = 1.


3



1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82, 83
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OFFSET

1,2


COMMENTS

Let x be the solution of 1/x + 1/(x+1)^2 = 1. Then (floor(n x) and (floor(n (x+1)^2))) 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.
Differs from A047201 first at A047201(85)=106, a(85)=105.  R. J. Mathar, Jan 11 2020


LINKS

Table of n, a(n) for n=1..67.
Eric Weisstein's World of Mathematics, Beatty Sequence.
Index entries for sequences related to Beatty sequences


FORMULA

a(n) = floor(n*x), where x = 1.24697960371... is the constant in A255249.


MAPLE

A330002 := proc(n)
local x;
x := 2*cos(5*Pi/7) ;
floor(n*x) ;
end proc: # R. J. Mathar, Jan 11 2020


MATHEMATICA

r = x /. FindRoot[1/x + 1/(x+1)^2 == 1, {x, 2, 10}, WorkingPrecision > 120]
RealDigits[r][[1]] (* A255249 *)
Table[Floor[n*r]], {n, 1, 250}] (* A330002 *)
Table[Floor[n*(1+r)^2], {n, 1, 250}] (* A330003 *)


CROSSREFS

Cf. A329825, A255249, A330003 (complement).
Sequence in context: A001961 A020656 A039116 * A047201 A225496 A261189
Adjacent sequences: A329999 A330000 A330001 * A330003 A330004 A330005


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jan 04 2020


STATUS

approved



