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

0,4

Links

Table of n, a(n) for n=0..74.

Ron Knott, Fibonacci Numbers, the Golden Section and the Golden String.

Eric Weisstein's World of Mathematics, Golden Ratio.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A007067, A001622, A099267, A029922.

Sequence in context: A367069 A078489 A194179 * A367068 A005379 A029922

Adjacent sequences: A101800 A101801 A101802 * A101804 A101805 A101806

Keyword

nonn

Author

Casey Mongoven, Jan 27 2005

Status

approved