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 A071986 Parity of the prime-counting function pi(n). 6
 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) + a(n-1) = 1 if and only if n is prime. - Benoit Cloitre, Jun 20 2002 LINKS Henri Lifchitz. Parity of Pi(n) Terence Tao et al., Prime counting function, Polymath1 project (2009) Terence Tao, Ernest Croot III, and Harald Helfgott, Deterministic methods to find primes, Math. Comp. 81 (2012), 1233-1246; arXiv:1009.3956, [math.NT], 2010-2012. FORMULA a(n) = pi(n) mod 2. a(n) = A000035(A000720(n)). - Omar E. Pol, Oct 26 2013 EXAMPLE a(6)=1 since three primes [2,3,5] are <= 6 and three is odd. MATHEMATICA Table[Mod[PrimePi[w], 2], {w, 1, 256}] PROG (PARI) a(n)=primepi(n)%2 (PARI) sq(n)=if (n<6, return(max(n-1, 0))); my(s, t); forsquarefree(i=1, sqrtint(n), t=n\i[1]^2; s+=moebius(i)*sum(i=1, sqrtint(t), t\i)); s; a(n)=my(s); forsquarefree(i=1, logint(n, 2), s+=moebius(i)*sq(sqrtnint(n, i[1]))); s%2 \\ Charles R Greathouse IV, Jan 09 2018 CROSSREFS Cf. A000720. Sequence in context: A104893 A104894 A168393 * A079944 A059652 A108736 Adjacent sequences:  A071983 A071984 A071985 * A071987 A071988 A071989 KEYWORD nonn,easy AUTHOR Labos Elemer, Jun 17 2002 EXTENSIONS Edited by Charles R Greathouse IV, Feb 19 2011 STATUS approved

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Last modified September 22 22:42 EDT 2018. Contains 315270 sequences. (Running on oeis4.)