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A005171
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0 if n is prime else 1.
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22
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1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Number of orbits of length n in map whose periodic points are A023890. - Thomas Ward (t.ward(AT)uea.ac.uk)
Characteristic function of nonprimes A018252. - Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 30 2007
Triangle A157423 = A005171 in every column. A052284 = INVERT transform of A005171, and the eigensequence of triangle A157423. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 28 2009]
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REFERENCES
| Yash Puri and Thomas Ward, A dynamical property unique to the Lucas sequence, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402.
Douglas Hofstadter, Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought.
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LINKS
| Index entries for characteristic functions
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
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FORMULA
| If b(n) is the n-th term of A023890, then a(n)=(1/n)* Sum_{ d divides n } \mu(d)a(n/d) E.g. a(6) = 1 since the 6th term of A023890 is 7 and the first term is 1.
a(n)=1-[(n-1)!^2 mod n], with n>=1. - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 11 2007
a(n) = NOT(A010051(n)) = 1 - A010051(n). - Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 30 2007
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MATHEMATICA
| f[n_] := If[PrimeQ@ n, 0, 1]; Array[f, 105] (* Robert G. Wilson v, June 20 2011 *)
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PROG
| (PARI) a(n)=if(n<1, 0, !isprime(n)) /* Michael Somos Jun 08 2005 */
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CROSSREFS
| Cf. A010051, A018252, A023890.
A157423, A157424, A052284 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 28 2009]
Sequence in context: A100810 A114591 A174889 * A076404 A010059 A143580
Adjacent sequences: A005168 A005169 A005170 * A005172 A005173 A005174
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KEYWORD
| nonn,easy
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AUTHOR
| Russ Cox (rsc(AT)swtch.com)
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EXTENSIONS
| More terms from Scott C. Lindhurst (ScottL(AT)alumni.princeton.edu)
Typo in crossrefs corrected - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 23 2010
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