

A330116


Beatty sequence for sinh(x), where 1/e^x + csch(x) = 1.


3



1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 31, 33, 34, 36, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 76, 78, 79, 81, 82, 84, 85, 87, 88, 89, 91, 92, 94, 95
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OFFSET

1,2


COMMENTS

Let x be the positive solution of 1/e^x + csch(x) = 1. Then (floor(n e^x) and (floor(n sinh(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



FORMULA

a(n) = floor(n sinh(x)), where x = 1.1676157... is the constant in A330115.


MATHEMATICA

r = x /. FindRoot[1/E^x + Csch[x] == 1, {x, 1, 2}, WorkingPrecision > 200]
Table[Floor[n*E^r], {n, 1, 250}] (* A330115 *)
Table[Floor[n*Sinh[r]], {n, 1, 250}] (* A330116 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



