

A007514


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


40



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

Hans Havermann, Table of n, a(n) for n = 0..10000
Index entries for sequences related to the number Pi


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

Essentially same as A075874.
Pi in base n: A004601 to A004608, A000796, A068436 to A068440, A062964.
Sequence in context: A158678 A117980 A065032 * A151671 A267502 A296605
Adjacent sequences: A007511 A007512 A007513 * A007515 A007516 A007517


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Robert G. Wilson v


STATUS

approved



