%I A010051
%S A010051 0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,
%T A010051 0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,
%U A010051 0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0
%N A010051 Characteristic function of primes: 1 if n is prime else 0.
%C A010051 The following sequences all have the same parity (with an extra zero 
               term at the start of A010051): A010051, A061007, A035026, A069754, 
               A071574. - Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Aug 
               09 2002
%C A010051 Let M(n) be the n X n matrix m(i,j)=0 if n divides ij+1, m(i,j)=1 otherwise; 
               then for n>0 a(n)=-det(M(n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Jan 17 2003
%C A010051 a(m*n) = a(m)*0^(n-1) + a(n)*0^(m-1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Nov 25 2004
%C A010051 a(n)=1 if n has no divisors other than 1 and n and 0 is n has at least 
               one divisor other than 1 and n. - Jon Perry (perry(AT)globalnet.co.uk), 
               Jul 02 2005
%C A010051 Equals A051731(the inverse Mobius transform) * A143519. [From Gary W. 
               Adamson (qntmpkt(AT)yahoo.com), Aug 22 2008]
%C A010051 Partial sums of a(n) in A000720. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 
               Mar 23 2009]
%D A010051 J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 
               2003, p. 3.
%D A010051 V. Brun, Ueber das Goldbachsche Gesetz und die Anzahl der Primzahlpaare, 
               Arch. Mat. Natur. B, 34, no. 8, 1915.
%D A010051 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 
               65.
%H A010051 Daniel Forgues, <a href="b010051.txt">Table of n, a(n) for n = 1..100000</
               a>
%H A010051 Y. Motohashi, <a href="http://arXiv.org/abs/math.NT/0505521">An overview 
               of Sieve Method and its History</a>
%H A010051 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A010051 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeConstant.html">Link to a section of The World of Mathematics.</
               a>
%H A010051 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeZetaFunction.html">Prime zeta function primezeta(s)</a>.
%H A010051 <a href="Sindx_Ch.html#char_fns">Index entries for characteristic functions</
               a>
%F A010051 a(n)= floor(cos(Pi*((n-1)!+1)/n)^2) for n>=2. - Antonio G. Astudillo 
               (afg_astudillo(AT)hotmail.com), Nov 07 2002
%F A010051 n>=2, a(n)=floor(phi(n)/(n-1))=floor(A000010(n)/(n-1)) - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Apr 11 2003
%F A010051 a(n) = Sum[d|gcd(n, A034386(n)), moebius(d) ] (Brun).
%F A010051 Dirichlet generating function: primezeta(s). - Franklin T. Adams-Watters, 
               Sep 11 2005.
%F A010051 a(n) = (n-1)!^2 mod n. - Franz Vrabec (franz.vrabec(AT)aon.at), Jun 24 
               2006
%F A010051 a(n) = A047886(n,1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Apr 15 2008
%F A010051 a(n) = A051731((n+1)!+1,n) from Wilson's theorem : n is prime iff (n+1)! 
               is congruent to -1 mod n. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), 
               Jan 20 2009, Jan 29 2009
%F A010051 a(n)=A166260/A001477. [From Mats Granvik (mats.granvik(AT)abo.fi), Oct 
               10 2009]
%p A010051 a := i->if isprime(i) then 1 else 0; fi;
%t A010051 Table[ If[ PrimeQ[n], 1, 0], {n, 105}] (from Robert G. Wilson v Jan 15 
               2005)
%o A010051 (MAGMA) s:=[]; for n in [1..100] do if IsPrime(n) then s:=Append(s,1); 
               else s:=Append(s,0); end if; end for; s;
%o A010051 (PARI) { for (n=1, 20000, if (isprime(n), a=1, a=0); write("b010051.txt", 
               n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Jun 15 2009]
%Y A010051 A051006 gives the decimal constant .414682509851... (base 10) = .01101010001010001010001... 
               (base 2).
%Y A010051 A001221 is the inverse Moebius transform of A010051 since it counts prime-divisors. 
               A010051 is the Moebius transform of A001221. - Labos E. (labos(AT)ana.sote.hu), 
               Jul 20 2001
%Y A010051 A143519 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 22 2008]
%Y A010051 A156660, A156659, A156657, A059500, A053176, A059456. [From Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 18 2009]
%Y A010051 Cf. A000720. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 
               23 2009]
%Y A010051 Sequence in context: A118247 A122257 A129950 this_sequence A131929 A100821 
               A139689
%Y A010051 Adjacent sequences: A010048 A010049 A010050 this_sequence A010052 A010053 
               A010054
%K A010051 nonn
%O A010051 1,1
%A A010051 N. J. A. Sloane (njas(AT)research.att.com).