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A322333
Factorial expansion of log(5) = Sum_{n>=1} a(n)/n!.
5
1, 1, 0, 2, 3, 0, 5, 4, 4, 8, 3, 3, 2, 0, 7, 8, 0, 7, 11, 1, 18, 16, 3, 10, 16, 21, 17, 13, 20, 12, 16, 8, 27, 24, 28, 12, 9, 34, 21, 3, 9, 8, 41, 42, 35, 31, 4, 4, 37, 38, 9, 20, 10, 31, 24, 34, 44, 21, 16, 19, 24, 4, 22, 22, 47, 8, 28, 26, 32, 22, 28, 56, 44, 16, 61, 38, 3, 25, 52, 35, 73, 55, 8, 42, 25, 21, 62, 61, 7, 89, 5, 74, 89, 57, 33, 60, 13, 75, 95, 66
OFFSET
1,4
EXAMPLE
log(5) = 1 + 1/2! + 0/3! + 2/4! + 3/5! + 0/6! + 5/7! + 4/8! + ...
MATHEMATICA
With[{b = Log[5]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]]
PROG
(PARI) default(realprecision, 250); b = log(5); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", "))
(Magma) SetDefaultRealField(RealField(250)); [Floor(Log(5))] cat [Floor(Factorial(n)*Log(5)) - n*Floor(Factorial((n-1))*Log(5)) : n in [2..80]];
(Sage)
def a(n):
if (n==1): return floor(log(5))
else: return expand(floor(factorial(n)*log(5)) - n*floor(factorial(n-1)*log(5)))
[a(n) for n in (1..80)]
CROSSREFS
Cf. A016628 (decimal expansion), A016733 (continued fraction).
Cf. A067882 (log(2)), A322334 (log(3)), A068460 (log(7)), A068461 (log(11)).
Sequence in context: A066913 A090303 A277516 * A346615 A240667 A051444
KEYWORD
nonn
AUTHOR
G. C. Greubel, Dec 03 2018
STATUS
approved