A007514 Pi = Sum_{n >= 0} a(n)/n!.

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

Offset: 0

Author

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

Keywords

• nonn

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

Examples

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

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

Crossrefs

Essentially same as A075874.

Pi in base n: A004601 to A004608, A000796, A068436 to A068440, A062964.

Programs

Mathematica

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

PARI

x=Pi;vector(floor((y->y/log(y))(default(realprecision))),n,t=(n-1)!;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

Formula

a(n) = floor(n!*Pi) - n*floor((n-1)!*Pi) for all n > 0. - M. F. Hasler, Mar 20 2017