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A329994 Beatty sequence for 2^x, where 1/x^2 + 1/2^x = 1. 3
2, 4, 7, 9, 12, 14, 17, 19, 22, 24, 27, 29, 31, 34, 36, 39, 41, 44, 46, 49, 51, 54, 56, 59, 61, 63, 66, 68, 71, 73, 76, 78, 81, 83, 86, 88, 90, 93, 95, 98, 100, 103, 105, 108, 110, 113, 115, 118, 120, 122, 125, 127, 130, 132, 135, 137, 140, 142, 145, 147 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Let x be the solution of 1/x^2 + 1/2^x = 1. Then (floor(n x^2)) and (floor(n 2^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
Eric Weisstein's World of Mathematics, Beatty Sequence.
FORMULA
a(n) = floor(n*2^x), where x = 1.298192... is the constant in A329992.
MATHEMATICA
r = x /. FindRoot[1/x^2 + 1/2^x == 1, {x, 1, 10}, WorkingPrecision -> 120]
RealDigits[r][[1]] (* A329992 *)
Table[Floor[n*r^2], {n, 1, 250}] (* A329993 *)
Table[Floor[n*2^r], {n, 1, 250}] (* A329994 *)
CROSSREFS
Cf. A329825, A329992, A329993 (complement).
Sequence in context: A059542 A190324 A022840 * A064995 A329846 A067839
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 02 2020
EXTENSIONS
Formula corrected. - R. J. Mathar, Jan 24 2020
STATUS
approved

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Last modified March 29 05:28 EDT 2024. Contains 371264 sequences. (Running on oeis4.)