

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
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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



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((n1)!*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((n1))*Log(Pi(R))) : n in [2..30]]; // G. C. Greubel, Mar 21 2018


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



