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A068446 Factorial expansion of sqrt(5) = Sum_{n>0} a(n)/n!. 4

%I #17 Sep 08 2022 08:45:05

%S 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,

%T 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,

%U 17,51,55,31,18,52,37,55,0,45,61,16,41,62,53,20,31,49,63,62,20,69,1,64

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

%H G. C. Greubel, <a href="/A068446/b068446.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Factorial_number_system#Fractional_values">Factorial number system: Fractional values</a>

%H <a href="/index/Fa#facbase">Index to sequences related to factorial base representation of noninteger constants</a>.

%t 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 *)

%o (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

%o (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

%o (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

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

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Mar 10 2002

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)