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Search: id:A002307
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| A002307 |
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Consecutive quadratic residues mod p: a(n)=maximal number of positive reduced quadratic residues which appear consecutively for n-th prime.
(Formerly M0418 N0160)
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+0
5
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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
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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When prime(n) == 3 (mod 4), then a(n)=A002308(n). - T. D. Noe, Apr 03 2007
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
A. A. Bennett, Consecutive quadratic residues, Bull. Amer. Math. Soc., 32 (1926), 283-284.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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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}] (from Robert G. Wilson v Jul 28 2004)
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CROSSREFS
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Cf. A002308.
Cf. A097159
Sequence in context: A023574 A131340 A098534 this_sequence A029247 A053269 A163873
Adjacent sequences: A002304 A002305 A002306 this_sequence A002308 A002309 A002310
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net)
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