A164629 Expansion of phi (golden ratio) in base 5.

1, 3, 0, 2, 1, 1, 1, 3, 4, 2, 3, 0, 4, 1, 2, 0, 2, 4, 2, 2, 3, 1, 4, 4, 3, 1, 1, 4, 0, 2, 0, 4, 0, 2, 1, 2, 1, 1, 1, 0, 3, 3, 1, 3, 3, 0, 4, 0, 0, 4, 0, 2, 4, 1, 0, 2, 2, 3, 0, 1, 1, 0, 4, 3, 4, 2, 2, 2, 1, 4, 4, 2, 1, 2, 1, 1, 4, 4, 3, 2, 2, 2, 1, 0, 3, 1, 2, 4, 1, 0

Offset: 1

Author

Keith Rarick, Dan McCandless (kr(AT)xph.us), Aug 18 2009

Keywords

• nonn
• base
• cons

Crossrefs

Cf. A001622, A004714.

Programs

Mathematica

RealDigits[(1 + Sqrt[5])/2, 5, 90]
RealDigits[GoldenRatio,5,120][[1]] (* Harvey P. Dale, Jan 19 2021 *)

PARI

default(realprecision, 1000); x=(1+sqrt(5))/2;
for(n=1, 100, d=floor(x); x=(x-d)*5; print1(d, ", ")); \\ Jinyuan Wang, Mar 21 2020

PARI

a(n) = floor(quadgen(5)*5^(n-1))%5 \\ Chittaranjan Pardeshi, Feb 06 2023