A101803 Nearest integer to n*(phi-1), where phi is golden ratio 1.618033988749895... (A001622).

0, 1, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 41, 42, 43, 43, 44, 44, 45, 46

Offset: 0

Author

Casey Mongoven, Jan 27 2005

Keywords

• nonn

Links

• Ron Knott, Fibonacci Numbers, the Golden Section and the Golden String.
• Eric Weisstein's World of Mathematics, Golden Ratio.

Crossrefs

Cf. A007067, A001622, A099267, A029922.

Programs

Mathematica

Table[Round[n(GoldenRatio-1)],{n,0,80}] (* Harvey P. Dale, Jun 12 2022 *)

PARI

a(n) = round(n*(sqrt(5)-1)/2); \\ Michel Marcus, May 23 2020

Formula

a(n) = round(n*phi) where phi is the smaller golden ratio value, .618033988749895....