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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 Hans Havermann, Table of n, a(n) for n = 0..10000 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 STATUS approved

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Last modified December 6 21:00 EST 2022. Contains 358648 sequences. (Running on oeis4.)