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 A115788 a(n) = floor(n*Pi) mod 2. 4
 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS The arithmetic mean (1/(n+1))*Sum_{k=0...n} a(k) converges to 1/2. What is effectively the same: the Cesaro limit (C1) of a(n) is 1/2. When we pick a term of the sequence at random, the probability of getting a '1' is 1/2. If we select a '1' randomly, the probability p11 of finding a '1' as the next term right of it is p11 = Pi - 3. If we select a '1' randomly, the probability p10 of finding a '0' as the next term right of it is p10 = 4 - Pi. Analogous statements hold for '0' --> '0' (p00 = p11) and '0' --> '1' (p01 = p10). First differs from A195062 at a(113). - Alois P. Heinz, Jan 22 2012 LINKS FORMULA a(n) = floor(n*Pi) mod 2. EXAMPLE a(2) = 0 because floor(2*Pi) = floor(6.28... ) = 6, a(8) = 1 because floor(8*Pi) = floor(25.13...) = 25. MAPLE a:= proc(n) Digits:= length(n) +15; floor(n*Pi) mod 2 end: seq(a(n), n=1..150);  # Alois P. Heinz, Jan 22 2012 MATHEMATICA Floor[Mod[\[Pi] Range[110], 2]]  (* Harvey P. Dale, Apr 02 2011 *) CROSSREFS Cf. A022844, A063438, A115789, A115790. Cf. A195062. - Alois P. Heinz, Jan 22 2012 Sequence in context: A285592 A276793 A284364 * A195062 A229940 A179761 Adjacent sequences:  A115785 A115786 A115787 * A115789 A115790 A115791 KEYWORD nonn AUTHOR Hieronymus Fischer, Jan 31 2006 STATUS approved

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Last modified April 23 01:55 EDT 2021. Contains 343198 sequences. (Running on oeis4.)