A329978 Beatty sequence for log x, where 1/x + 1/(log x) = 1.

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, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 58, 59, 60, 62, 63, 64, 66, 67

Offset

1,2

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. A236229, A329825, A329977 (complement).

Sequence in context: A004773 A104401 A184421 * A329839 A039070 A059553

Adjacent sequences: A329975 A329976 A329977 * A329979 A329980 A329981

Keyword

nonn,easy

Author

Clark Kimberling, Jan 02 2020

Status

approved