A334415 Nearest integer to n*(2-phi), where phi is the golden ratio (A001622).

0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27

Offset

0,5

Links

Table of n, a(n) for n=0..71.

Formula

a(n) = round(n*(2-phi)).

a(n) = n - A101803(n).

Example

a(0) = round(0*(2-phi)) = round(0) = 0.
a(1) = round(1*(2-phi)) = round(0.382) = 0.
a(2) = round(2*(2-phi)) = round(0.764) = 1.

Mathematica

a[n_] := Round[n * (2 - GoldenRatio)]; Array[a, 72, 0] (* Amiram Eldar, Jun 14 2020 *)

Prog

(PARI) a(n) = round(n*(2-(1+sqrt(5))/2)); \\ Michel Marcus, Jun 14 2020

Crossrefs

Cf. A001622, A101803, A132338 (2-phi), A334414, A334413.

Sequence in context: A026405 A226033 A054404 * A307152 A008671 A199017

Adjacent sequences: A334412 A334413 A334414 * A334416 A334417 A334418

Keyword

nonn

Author

Aresh Pourkavoos, Apr 30 2020

Status

approved