A248515 -id:A248515 - cp's OEIS frontend

A022840 Beatty sequence for sqrt(6).

2, 4, 7, 9, 12, 14, 17, 19, 22, 24, 26, 29, 31, 34, 36, 39, 41, 44, 46, 48, 51, 53, 56, 58, 61, 63, 66, 68, 71, 73, 75, 78, 80, 83, 85, 88, 90, 93, 95, 97, 100, 102, 105, 107, 110, 112, 115, 117, 120, 122, 124, 127, 129, 132, 134, 137, 139, 142, 144, 146

Offset: 1

Clark Kimberling

nonn

Complement of A138235; a(n) = A138236(A138235(n)) and A138236(a(n)) = A138235(n). - Reinhard Zumkeller, Mar 07 2008

Numbers k such that A248515(k+1) = A248515(k) + 1 = 1 + least number h such that 1 - h*sin(1/h) < 1/n^2. The difference sequence of A248515 is (0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, ...), so that A138235 = (1, 3, 5, 6, 8, ...) and A022840 = (2, 4, 7, 9, 12, 14, ...). - Clark Kimberling, Jun 16 2015

Iain Fox, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)
Clark Kimberling, Beatty sequences and trigonometric functions, Integers 16 (2016), #A15.
Eric Weisstein's World of Mathematics, Beatty Sequence
Index entries for sequences related to Beatty sequences

Cf. A010464 (sqrt(6)), A138235 (complement), A248515.

a022840 = floor . (* sqrt 6) . fromIntegral
-- Reinhard Zumkeller, Sep 14 2014

[Floor(n*Sqrt(6)): n in [1..60]]; // Vincenzo Librandi, Jun 17 2015

Table[Floor[n Sqrt[6]], {n, 70}] (* Vincenzo Librandi, Jun 17 2015 *)

a(n) = floor(n*sqrt(6)) \\ Iain Fox, Nov 20 2017

A138235 a(n) = floor(n*(6 + sqrt(6))/5).

Original entry on oeis.org

1, 3, 5, 6, 8, 10, 11, 13, 15, 16, 18, 20, 21, 23, 25, 27, 28, 30, 32, 33, 35, 37, 38, 40, 42, 43, 45, 47, 49, 50, 52, 54, 55, 57, 59, 60, 62, 64, 65, 67, 69, 70, 72, 74, 76, 77, 79, 81, 82, 84, 86, 87, 89, 91, 92, 94, 96, 98, 99, 101, 103, 104, 106, 108, 109, 111, 113, 114

Offset: 1

Reinhard Zumkeller, Mar 07 2008

nonn

Beatty sequence for (6+sqrt(6))/5; complement of A022840;
a(n) = A138236(A022840(n)) and A138236(a(n)) = A022840(n).
Numbers k such that A248515(k+1) = A248515(k) = least number h such that 1 - h*sin(1/h) < 1/n^2. The difference sequence of A248515 is (0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, ...), so that A138235 = (1, 3, 5, 6, 8, ...) and A022840 = (2, 4, 7, 9, 12, 14, ...). - Clark Kimberling, Jun 16 2015

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Clark Kimberling, Beatty sequences and trigonometric functions, Integers 16 (2016), #A15.
Eric Weisstein's World of Mathematics, Beatty Sequence
Index entries for sequences related to Beatty sequences

Cf. A248515, A022840 (complement).

[Floor(n*(6+Sqrt(6))/5): n in [1..70]]; // Vincenzo Librandi, Jun 17 2015

With[{c=6+Sqrt[6]},Table[Floor[(n*c)/5],{n,80}]] (* Harvey P. Dale, Feb 25 2013 *)

cp's OEIS Frontend

A022840 Beatty sequence for sqrt(6).

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