A101803 - OEIS

%I #13 Jun 12 2022 13:30:27

%S 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,

%T 17,18,19,19,20,20,21,22,22,23,23,24,25,25,26,27,27,28,28,29,30,30,31,

%U 32,32,33,33,34,35,35,36,36,37,38,38,39,40,40,41,41,42,43,43,44,44,45,46

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

%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html">Fibonacci Numbers, the Golden Section and the Golden String</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldenRatio.html">Golden Ratio</a>.

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

%t Table[Round[n(GoldenRatio-1)],{n,0,80}] (* _Harvey P. Dale_, Jun 12 2022 *)

%o (PARI) a(n) = round(n*(sqrt(5)-1)/2); \\ _Michel Marcus_, May 23 2020

%Y Cf. A007067, A001622, A099267, A029922.

%K nonn

%O 0,4

%A _Casey Mongoven_, Jan 27 2005