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A329993 Beatty sequence for x^2, where 1/x^2 + 1/2^x = 1. 3
1, 3, 5, 6, 8, 10, 11, 13, 15, 16, 18, 20, 21, 23, 25, 26, 28, 30, 32, 33, 35, 37, 38, 40, 42, 43, 45, 47, 48, 50, 52, 53, 55, 57, 58, 60, 62, 64, 65, 67, 69, 70, 72, 74, 75, 77, 79, 80, 82, 84, 85, 87, 89, 91, 92, 94, 96, 97, 99, 101, 102, 104, 106, 107 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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*x^2), where x = 1.29819... is the constant in A329992; a(n) first differs from A064994(n) at n=89.
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, A329994 (complement).
Sequence in context: A244644 A047220 A329845 * A064994 A138235 A329833
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 02 2020
STATUS
approved

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Last modified February 21 03:13 EST 2024. Contains 370219 sequences. (Running on oeis4.)