OFFSET
1,5
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000 (terms 1..300 from Vincenzo Librandi)
Wikipedia, Factorial number system
FORMULA
a(n) = floor(c*n!) - n*floor(c*(n-1)!) = floor(frac(c*(n-1)!)*n) for n > 1, with c = zeta(5). - M. F. Hasler, Dec 20 2018
MATHEMATICA
t = Zeta[5]; s = {}; Do[n = Floor[t*i!]; t -= n/i!; AppendTo[s, n], {i, 1, 30}]; s (* Amiram Eldar, Nov 25 2018 *)
With[{b = Zeta[5]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* G. C. Greubel, Nov 26 2018 *)
PROG
(PARI) vector(N=100, n, if(n>1, c=c%1*n, c=zeta(precision(5., N*log(N/2.7)\2.3+3)))\1) \\ Specific a(n) can be computed via the FORMULA. For repeated use the value of c can be stored as a global variable, to be re-computed with higher precision when log_10(n!) exceeds its precision. - M. F. Hasler, Nov 25 2018
(Magma) SetDefaultRealField(RealField(250)); b:=Evaluate(RiemannZeta(), 5); [n eq 1 select Floor(b) else Floor(Factorial(n)*b) - n*Floor(Factorial(n)*b/n) : n in [1..100]]; // G. C. Greubel, Nov 26 2018
(Sage)
b=zeta(5)
@cached_function
def A068454(n):
if n == 1: return floor(b)
else: return expand(floor(factorial(n)*b) - n*floor(factorial(n-1)*b))
[A068454(n) for n in (1..100)] # G. C. Greubel, Nov 26 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Mar 10 2002
EXTENSIONS
Name edited and keyword cons removed by M. F. Hasler, Nov 25 2018
STATUS
approved