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Search: id:A034947
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| A034947 |
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Jacobi (or Kronecker) symbol (-1/n). |
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+0
3
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| 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also the regular paper-folding sequence.
Comment from Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Nov 08, 2004: It appears that, replacing +1 with 0 and -1 with 1, we obtain A038189. Alternatively, replacing -1 with 0 we obtain (allowing for offset) A014577.
Partial sums = A005811 starting (1, 2, 1, 2, 3, 2, 1, 2, 3,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 23 2008
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REFERENCES
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J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 155.
H. Cohen, Course in Computational Number Theory, p. 28.
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LINKS
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Joerg Arndt, Fxtbook
Eric Weisstein's World of Mathematics, Kronecker Symbol
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FORMULA
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Multiplicative with a(2^e) = 1, a(p^e) = (-1)^(e(p-1)/2) if p>2.
a(2n)=a(n), a(4n+1)=1, a(4n+3)=-1, a(-n)=-a(n). a(n)=2*A014577(n-1)-1.
a(prime(n)) = A070750(n) for n > 1 - T. D. Noe (noe(AT)sspectra.com), Nov 08 2004
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MAPLE
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with(numtheory): A034947 := n->jacobi(-1, n);
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MATHEMATICA
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Needs["NumberTheory`"]; Table[KroneckerSymbol[ -1, n], {n, 0, 100}]
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PROGRAM
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(PARI) a(n)=kronecker(-1, n)
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CROSSREFS
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Cf. A005811.
Sequence in context: A108784 A010555 A020985 this_sequence A097807 A014077 A165326
Adjacent sequences: A034944 A034945 A034946 this_sequence A034948 A034949 A034950
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KEYWORD
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sign,nice,easy,mult
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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