

A329978


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


3



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
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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 A2362296.


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, 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



