0,2

This Egyptian expansion is produced using a greedy rule.

Table of n, a(n) for n=0..8.

a(0)=1 since 1/phi is between 1/1 and 1/2 and 1/1 > 1/phi; i.e., floor(1/(1/phi)) = 1.

a(1)=2 since floor(1/(1/a(0) - 1/phi)) = 2.

a(2)=8 since floor(1/(1/phi - (1/a(0)-1/(a(1)))) = 8, and so on.

Cf. A117116, A014015, A014013.

Sequence in context: A259126 A140050 A318038 * A154908 A166356 A009817

Adjacent sequences: A304795 A304796 A304797 * A304799 A304800 A304801

easy,frac,nonn

Greg Huber, May 18 2018

approved