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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 (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
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified May 18 15:59 EDT 2024. Contains 372664 sequences. (Running on oeis4.)