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A329991
Beatty sequence for 3^x, where 1/x + 1/3^x = 1.
3
2, 4, 7, 9, 12, 14, 17, 19, 22, 24, 27, 29, 32, 34, 37, 39, 42, 44, 47, 49, 52, 54, 57, 59, 62, 64, 66, 69, 71, 74, 76, 79, 81, 84, 86, 89, 91, 94, 96, 99, 101, 104, 106, 109, 111, 114, 116, 119, 121, 124, 126, 128, 131, 133, 136, 138, 141, 143, 146, 148
OFFSET
1,1
COMMENTS
Let x be the solution of 1/x + 1/3^x = 1. Then (floor(n x)) 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 x), where x = 1.31056994... is the constant in A329989.
MATHEMATICA
r = x /. FindRoot[1/x + 1/3^x == 1, {x, 1, 10}, WorkingPrecision -> 120]
RealDigits[r][[1]] (* A329989 *)
Table[Floor[n*r], {n, 1, 250}] (* A329990 *)
Table[Floor[n*2^r], {n, 1, 250}] (* A329991 *)
CROSSREFS
Cf. A329825, A329989, A329990 (complement).
Sequence in context: A064995 A329846 A067839 * A047211 A225000 A189677
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 02 2020
STATUS
approved