

A007514


Pi = Sum_{n >= 0} a(n)/n!.
(Formerly M2193)


32



3, 0, 0, 0, 3, 1, 5, 6, 5, 0, 1, 4, 7, 8, 0, 6, 7, 10, 7, 10, 4, 10, 6, 16, 1, 11, 20, 3, 18, 12, 9, 13, 18, 21, 14, 34, 27, 11, 27, 33, 36, 18, 5, 18, 5, 23, 39, 1, 10, 42, 28, 17, 20, 51, 8, 42, 47, 0, 27, 23, 16, 52, 32, 52, 53, 24, 43, 61, 64, 18, 17, 11, 0, 53, 14, 62
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OFFSET

0,1


COMMENTS

The current name does not define a(n) without ambiguity. It is meant that for each n, a(n) is the largest integer such that the remainder of Pi  (partial sum up to n) remains positive. This leads to the FORMULA given below.  M. F. Hasler, Mar 20 2017


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS



FORMULA

a(n) = floor(n!*Pi)  n*floor((n1)!*Pi) for all n > 0.  M. F. Hasler, Mar 20 2017


EXAMPLE

Pi = 3/0! + 0/1! + 0/2! + 0/3! + 3/4! + 1/5! + ...


MATHEMATICA

p = N[Pi, 1000]; Do[k = Floor[p*n! ]; p = p  k/n!; Print[k], {n, 0, 75} ]


PROG

(PARI) x=Pi; vector(floor((y>y/log(y))(default(realprecision))), n, t=(n1)!; k=floor(x*t); x=k/t; k) \\ Charles R Greathouse IV, Jul 15 2011
(PARI) C=1/Pi; x=0; vector(primepi(default(realprecision)), n, x*n+x=n!\C) \\ M. F. Hasler, Mar 20 2017


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



