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 A068448 Factorial expansion of log(Pi) = Sum_{n>0} a(n)/n! with a(n) as large as possible. 1
 1, 0, 0, 3, 2, 2, 1, 3, 4, 5, 8, 10, 11, 7, 13, 13, 3, 14, 11, 16, 6, 9, 3, 14, 0, 16, 22, 9, 8, 26, 5, 18, 6, 3, 13, 31, 4, 27, 25, 5, 12, 1, 17, 31, 2, 4, 16, 17, 39, 15, 15, 25, 52, 40, 50, 3, 27, 32, 54, 18, 55, 10, 29, 62, 38, 4, 17, 53, 13, 24, 22, 40, 23, 11, 74, 18, 74, 31, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS If a(n) is not required to be as large as possible, it isn't well defined: it can be decreased by any amount x without changing the value of the sum, if x*(n+1) is added to a(n+1), which in turn can be decreased by any arbitrary amount etc. - M. F. Hasler, Dec 04 2018 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. MATHEMATICA Table[If[n == 1, Floor[Log[Pi]], Floor[n!*Log[Pi]] - n*Floor[(n - 1)!*Log[Pi]]], {n, 1, 50}] (* G. C. Greubel, Mar 21 2018 *) PROG (PARI) for(n=1, 30, print1(if(n==1, floor(log(Pi)), floor(n!*log(Pi)) - n*floor((n-1)!*log(Pi))), ", ")) \\ G. C. Greubel, Mar 21 2018 (PARI) A068448_vec(N=90, c=log(precision(Pi, N*log(N/2.4)\/2.3)))=vector(N, n, if(n>1, c=c%1*n, c)\1) \\ N*log(N/2.4)\/2.3 ~ logint(N!, 10) but uses much less memory when N is big. - M. F. Hasler, Nov 28 2018 (Magma) R:= RealField(); [Floor(Log(Pi(R)))] cat [Floor(Factorial(n)*Log(Pi(R))) - n*Floor(Factorial((n-1))*Log(Pi(R))) : n in [2..30]]; // G. C. Greubel, Mar 21 2018 CROSSREFS Cf. A053510 (decimal expansion). Similar expansions: A068450 (sqrt(Pi)), A075874 (Pi), A007514 (a different variant for Pi). Sequence in context: A204257 A074976 A329873 * A054081 A164585 A200996 Adjacent sequences: A068445 A068446 A068447 * A068449 A068450 A068451 KEYWORD nonn AUTHOR Benoit Cloitre, Mar 10 2002 EXTENSIONS Name edited by M. F. Hasler, Dec 04 2018 STATUS approved

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Last modified December 9 12:57 EST 2023. Contains 367690 sequences. (Running on oeis4.)