A195607 - OEIS

%I #17 Apr 14 2023 17:42:02

%S 1,8,161,809,809,161803,1618033,16180339,80901699,404508497,

%T 16180339887,80901699437,1618033988749,8090169943749,161803398874989,

%U 809016994374947,4045084971874737,40450849718747371,25281781074217107,8090169943749474241

%N Numerator of floor(Phi*10^n)/10^n, where phi = (sqrt(5) + 1)/2 = A001622 is the Golden Ratio.

%C Numerator of the decimal fraction of phi = 1.61803... truncated to a given number of decimal places.

%C The corresponding sequence for 1/phi = 0.61803... = phi-1 (also called the Golden Ratio) has a very similar behavior, because for both, the truncated decimal expansion can be simplified by the same factors 2^k*5^m.

%e a(3) = 161 is the numerator of 1.61 = 161/100.

%e a(4) = 809 is the numerator of 1.618 = 1618/1000 = 809/500.

%t Floor[GoldenRatio #]/#&/@(10^Range[0,20])//Numerator (* _Harvey P. Dale_, Apr 14 2023 *)

%o (PARI) a(n,c=sqrt(5)/2+.5)=numerator(c\.1^n/10^n)  \\ _M. F. Hasler_, Sep 21 2011

%Y Cf. A001622, A011551.

%Y Cf. A195603 (analog for Pi), A195604 (for e), A195606 (for gamma).

%K nonn,base

%O 0,2

%A _M. F. Hasler_, following a suggestion by _Eric Angelini_, Sep 21 2011