A007514 - OEIS

A007514

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

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

(list; graph; refs; listen; history; text; internal format)

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((n-1)!*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=(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

CROSSREFS

Essentially same as A075874.

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

Sequence in context: A158678 A117980 A065032 * A336642 A151671 A267502

Adjacent sequences: A007511 A007512 A007513 * A007515 A007516 A007517

KEYWORD

nonn

AUTHOR

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

STATUS

approved