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A002307
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Consecutive quadratic residues mod p: a(n) is the maximal number of positive reduced quadratic residues which appear consecutively for n-th prime.
(Formerly M0418 N0160)
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6
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1, 1, 1, 2, 3, 2, 2, 4, 4, 4, 4, 4, 3, 5, 4, 3, 5, 5, 6, 6, 4, 6, 7, 4, 4, 7, 7, 6, 5, 5, 7, 8, 6, 5, 4, 7, 6, 6, 6, 6, 6, 6, 6, 4, 7, 6, 7, 7, 7, 5, 6, 6, 6, 7, 6, 7, 8, 7, 10, 6, 9, 9, 7, 10, 5, 5, 8, 5, 8, 6, 6, 8, 9, 6, 8, 8, 8, 5, 7, 6, 8, 7, 6, 7, 10, 8, 8, 5, 8, 8, 11, 12, 8, 8, 10, 8, 9, 8, 10, 7, 9, 9, 10, 10, 7, 6, 9
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OFFSET
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1,4
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COMMENTS
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A048280(n) is defined similarly, except that reduced quadratic residues equal to 0 are also included. - Jonathan Sondow, Jul 20 2014
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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MATHEMATICA
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f[l_, a_] := Module[{A = Split[l], B}, B = Last[ Sort[ Cases[A, x : {a ..} :> {Length[x], Position[A, x][[1, 1]]}]]]; {First[B], Length[ Flatten[ Take[A, Last[B] - 1]]] + 1}]; g[n_] := f[ JacobiSymbol[ Range[ Prime[n] - 1], Prime[n]], 1][[1]]; Table[ g[n], {n, 2, 102}] (* Robert G. Wilson v, Jul 28 2004 *)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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