A277113 a(n) = floor(n/(1-Pi/(sqrt(5)+1))).

34, 68, 102, 137, 171, 205, 239, 274, 308, 342, 376, 411, 445, 479, 513, 548, 582, 616, 650, 685, 719, 753, 787, 822, 856, 890, 924, 959, 993, 1027, 1061, 1096, 1130, 1164, 1198, 1233, 1267, 1301, 1335, 1370, 1404, 1438, 1472, 1507, 1541, 1575, 1609, 1644, 1678

Offset

1,1

Comments

The goal is to generate a ratio near 1 from two well-known constants.

Links

Paulo Romero Zanconato Pinto, Table of n, a(n) for n = 1..10000

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n/(1-Pi/(sqrt(5)+1))).

Example

For n = 10 we have that floor(10/(1-Pi/(sqrt(5)+1))) = floor(10/0.02919448...) = floor(342.5304983...) so a(10) = 342.

Maple

A277113:=n->floor(n/(1-Pi/(sqrt(5)+1))): seq(A277113(n), n=1..100);

Mathematica

f[n_] := Floor[n/(1-Pi/(Sqrt[5]+1))]; Array[f, 100, 1]

Prog

(PARI) a(n) = n\(1-Pi/(sqrt(5)+1)) \\ Michel Marcus, Oct 29 2016

Crossrefs

Complement of A277112.

Cf. A000796, A001622, A094881, A094882.

Sequence in context: A259955 A259887 A028381 * A036180 A063331 A044136

Adjacent sequences: A277110 A277111 A277112 * A277114 A277115 A277116

Keyword

nonn

Author

Paulo Romero Zanconato Pinto, Sep 30 2016

Extensions

More terms from Michel Marcus, Oct 29 2016

Status

approved