A190511 n+[nr/u]+[ns/u]+[nt/u]; r=golden ratio, s=r^2, t=r^3, u=r^4.

1, 3, 5, 7, 10, 12, 14, 16, 19, 21, 23, 25, 28, 30, 32, 34, 37, 39, 41, 43, 45, 48, 50, 52, 54, 57, 59, 61, 63, 66, 68, 70, 72, 75, 77, 79, 81, 83, 86, 88, 90, 92, 95, 97, 99, 101, 104, 106, 108, 110, 113, 115, 117, 119, 121, 124, 126, 128, 130, 133, 135, 137, 139, 142, 144, 146, 148, 151, 153, 155, 157, 159, 162, 164, 166, 168, 171, 173

Offset: 1

Author

Clark Kimberling, May 11 2011

Keywords

• nonn

Comments

A190508: a(n)=n+[nr]+[nr^2]+[nr^3]

A190509: b(n)=[n/r]+n+[nr]+[nr^2]

A054770: c(n)=[n/r^2]+[n/r]+n+[nr]

A190511: d(n)=[n/r^3]+[n/r^2]+[n/r]+n

Are the differences between successive terms always 2 or 3? - Harvey P. Dale, Apr 03 2025

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A190508, A190509, A054770.

Programs

Mathematica

(See A190508.)
Module[{g=GoldenRatio,g4},g4=g^4;Table[n+Floor[(n*g)/g4]+Floor[(n*g^2)/g4]+Floor[(n*g^3)/g4],{n,80}]] (* Harvey P. Dale, Apr 03 2025 *)

Formula

a(n) = A022839(n)-1. - Michel Dekking, May 04 2019