A068446 Factorial expansion of sqrt(5) = Sum_{n>0} a(n)/n!.

2, 0, 1, 1, 3, 1, 6, 6, 2, 3, 5, 2, 12, 1, 7, 1, 3, 10, 12, 19, 10, 18, 21, 6, 3, 10, 10, 26, 18, 0, 26, 30, 5, 21, 21, 5, 28, 34, 22, 9, 28, 32, 0, 9, 19, 20, 8, 9, 16, 43, 28, 22, 4, 40, 54, 17, 51, 55, 31, 18, 52, 37, 55, 0, 45, 61, 16, 41, 62, 53, 20, 31, 49, 63, 62, 20, 69, 1, 64

Offset: 1

Author

Benoit Cloitre, Mar 10 2002

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Wikipedia, Factorial number system: Fractional values
• Index to sequences related to factorial base representation of noninteger constants.

Crossrefs

Cf. A002163 (decimal expansion of sqrt(5)).

Programs

Magma

[Floor(Sqrt(5))] cat [Floor(Factorial(n)*Sqrt(5)) - n*Floor(Factorial((n-1))*Sqrt(5)) : n in [2..30]]; // G. C. Greubel, Mar 21 2018

Mathematica

Table[If[n==1, Floor[Sqrt[5]],Floor[n!*Sqrt[5]]-n*Floor[(n-1)!*Sqrt[5] ]], {n,1,50}] (* G. C. Greubel, Mar 21 2018 *)

PARI

for(n=1,30, print1(if(n==1, floor(sqrt(5)), floor(n!*sqrt(5)) - n*floor((n-1)!*sqrt(5))), ", ")) \\ G. C. Greubel, Mar 21 2018

PARI

A068446_vec(N=90,c=sqrt(precision(5.,N*log(N/2.4)\/2.3)))=vector(N,n, if(n>1,c=c%1*n,c)\1) \\ M. F. Hasler, Nov 27 2018