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Search: id:A010051
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| A010051 |
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Characteristic function of primes: 1 if n is prime else 0. |
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+0
65
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| 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, 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, 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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
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
a(m*n) = a(m)*0^(n-1) + a(n)*0^(m-1). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Nov 25 2004
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
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REFERENCES
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J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 3.
V. Brun, Ueber das Goldbachsche Gesetz und die Anzahl der Primzahlpaare, Arch. Mat. Natur. B, 34, no. 8, 1915.
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 65.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..10000
Y. Motohashi, An overview of Sieve Method and its History
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Prime zeta function primezeta(s).
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FORMULA
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a(n)= floor(cos(Pi*((n-1)!+1)/n)^2) for n>=2. - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 07 2002
n>=2, a(n)=floor(phi(n)/(n-1))=floor(A000010(n)/(n-1)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 11 2003
a(n) = Sum[d|gcd(n, A034386(n)), moebius(d) ] (Brun).
Dirichlet generating function: primezeta(s). - Franklin T. Adams-Watters, Sep 11 2005.
a(n) = (n-1)!^2 mod n. - Franz Vrabec (franz.vrabec(AT)planetuniqa.at), Jun 24 2006
a(n) = A047886(n,1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 15 2008
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MAPLE
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a := i->if isprime(i) then 1 else 0; fi;
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MATHEMATICA
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Table[ If[ PrimeQ[n], 1, 0], {n, 105}] (from Robert G. Wilson v Jan 15 2005)
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PROGRAM
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(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;
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CROSSREFS
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A051006 gives the decimal constant .414682509851... (base 10) = .01101010001010001010001... (base 2).
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
Adjacent sequences: A010048 A010049 A010050 this_sequence A010052 A010053 A010054
Sequence in context: A118247 A122257 A129950 this_sequence A131929 A100821 A073070
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KEYWORD
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nonn,new
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AUTHOR
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njas
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