A329977 Beatty sequence for the number x satisfying 1/x + 1/(log x) = 1.

3, 7, 11, 15, 19, 23, 27, 30, 34, 38, 42, 46, 50, 54, 57, 61, 65, 69, 73, 77, 81, 84, 88, 92, 96, 100, 104, 108, 111, 115, 119, 123, 127, 131, 135, 138, 142, 146, 150, 154, 158, 162, 165, 169, 173, 177, 181, 185, 189, 192

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..50.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n x), where x = 3.8573348... is the constant in A236229.

Mathematica

r = x /. FindRoot[1/x + 1/Log[x] == 1, {x, 3, 4}, WorkingPrecision -> 210];
RealDigits[r][[1]]; (* A236229 *)
Table[Floor[n*r], {n, 1, 50}];       (* A329977 *)
Table[Floor[n*Log[r]], {n, 1, 50}];  (* A329978 *)

Crossrefs

Cf. A329825, A236229, A329978 (complement).

Sequence in context: A249244 A059554 A329840 * A246171 A184422 A254311

Adjacent sequences: A329974 A329975 A329976 * A329978 A329979 A329980

Keyword

nonn,easy

Author

Clark Kimberling, Jan 02 2020

Status

approved