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Search: id:A112046
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| A112046 |
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a(n) = first i >= 1 for which the Jacobi symbol J(i,2n+1) is not +1 (i.e. is either 0 or -1). |
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+0
9
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| 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 5, 5, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 5, 7, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 7, 5, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 5, 5, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 7, 11, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 5, 5, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 5, 13, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 7, 5, 2, 2, 3, 3, 2, 2
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If we instead list the first i >= 1, for which Jacobi symbol J(i,2n+1) is 0, we get A090368.
It is easy to see that every term is prime. Because the Jacobi symbol is multiplicative as J(ab,m) = J(a,m)*J(b,m) and if for every index i>=1 and < x, J(i,m)=1, then if J(x,m) is 0 or -1, x cannot be composite (say y*z, with both y and z less than x), as then either J(y,m) or J(z,m) would be non-one, which contradicts our assumption that x is the first index where non-one value appears. Thus x must be prime.
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CROSSREFS
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a(n)=A112050(n)+1. Bisections: A112047, A112048. Their difference: A112053. Cf. A112049, A112060, A112070.
Adjacent sequences: A112043 A112044 A112045 this_sequence A112047 A112048 A112049
Sequence in context: A055092 A130326 A059906 this_sequence A076902 A049113 A055093
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Aug 27 2005
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