A379511 a(n) = floor(n*(2^(1/4) + 2^(-1/4))); Beatty sequence for 2^(1/4) + 2^(-1/4).

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125

Offset

1,1

Comments

Let u = 2^(1/4) + 2^(-1/4) and v = u/(u-1); let b(n) = floor[n*v], so that (b(n)) is the Beatty sequence for v. Then (a(n)) and (b(n)) partition the positive integers. Also, 0 <= a(n) - A378142(n) <= 1 for every n.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for sequences related to Beatty sequences.

Formula

a(n) = floor(n*(2^(1/4) + 2^(-1/4))).

Mathematica

Table[Floor[n (2^(1/4) + 2^(-1/4))], {n, 1, 120}]

Crossrefs

Cf. A378142.

Sequence in context: A122080 A105360 A386725 * A306720 A084564 A053228

Adjacent sequences: A379508 A379509 A379510 * A379512 A379513 A379514

Keyword

nonn

Author

Clark Kimberling, Jan 11 2025

Status

approved