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A075874
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Pi = Sum a(n)/n!, n=1..inf.
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5
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3, 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; internal format)
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OFFSET
| 1,1
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LINKS
| Eric Weisstein's World of Mathematics, Harmonic Expansion
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FORMULA
| a(1)=3; for n>1 a(n) =floor(n!*Pi)-n*floor((n-1)!*Pi) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 10 2002
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EXAMPLE
| Pi = 3/1! + 0/2! + 0/3! + 3/4! + 1/5! + ...
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MAPLE
| Digits := 120; M := proc(a, n) local i, b, c; b := a; c := [ floor(b) ]; for i from 1 to n-1 do b := b-c[ i ]/i!; c := [ op(c), floor(b*(i+1)!) ]; od; c; end: t1 := M(Pi, 100); A075874 := n->t1[n+1];
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MATHEMATICA
| p = N[Pi, 1000]; Do[k = Floor[p*n! ]; p = p - k/n!; Print[k], {n, 1, 75} ]
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PROG
| (PARI) x=Pi; vector(floor((y->y/log(y))(default(realprecision))), n, t=n!; k=floor(x*t); x-=k/t; k) \\ Charles R Greathouse IV, Jul 15 2011
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CROSSREFS
| Essentially same as A007514.
Pi in base n: A004601 to A004608, A000796, A068436 to A068440, A062964.
Sequence in context: A021337 A033685 A063691 * A181634 A178952 A178153
Adjacent sequences: A075871 A075872 A075873 * A075875 A075876 A075877
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 02, 2001 and Oct 20, 2002
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