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A329997
Beatty sequence for 3^x, where 1/x^3 + 1/3^x = 1.
3
3, 6, 10, 13, 17, 20, 24, 27, 30, 34, 37, 41, 44, 48, 51, 54, 58, 61, 65, 68, 72, 75, 78, 82, 85, 89, 92, 96, 99, 102, 106, 109, 113, 116, 120, 123, 126, 130, 133, 137, 140, 144, 147, 150, 154, 157, 161, 164, 168, 171, 174, 178, 181, 185, 188, 192, 195, 198
OFFSET
1,1
COMMENTS
Let x be the solution of 1/x^3 + 1/3^x = 1. Then (floor(n*x^3)) and (floor(n*3^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.
FORMULA
a(n) = floor(n*3^x), where x = 1.12177497... is the constant in A329995.
MATHEMATICA
r = x /. FindRoot[1/x^3 + 1/3^x == 1, {x, 1, 10}, WorkingPrecision -> 120]
RealDigits[r][[1]] (* A329995 *)
Table[Floor[n*r^3], {n, 1, 250}] (* A329996 *)
Table[Floor[n*3^r], {n, 1, 250}] (* A329997 *)
CROSSREFS
Cf. A329825, A329995, A329996 (complement).
Sequence in context: A189795 A145383 A258834 * A194028 A047280 A310054
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 03 2020
STATUS
approved