The On-Line Encyclopedia of Integer Sequences (OEIS)

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A002307

Consecutive quadratic residues mod p: a(n) is the maximal number of positive reduced quadratic residues which appear consecutively for n-th prime.
(history; published version)

#27 by Jon E. Schoenfield at Wed Dec 22 00:09:26 EST 2021

STATUS

editing

approved

#26 by Jon E. Schoenfield at Wed Dec 22 00:09:23 EST 2021

NAME

Consecutive quadratic residues mod p: a(n)= is the maximal number of positive reduced quadratic residues which appear consecutively for n-th prime.

LINKS

T. D. Noe, <a href="/A002307/b002307.txt">Table of n, a(n) for n = 1..10000</a>

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#25 by Bruno Berselli at Mon Jul 21 04:33:03 EDT 2014

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proposed

approved

#24 by Joerg Arndt at Mon Jul 21 03:54:45 EDT 2014

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editing

proposed

#23 by Alonso del Arte at Sun Jul 20 17:25:15 EDT 2014

COMMENTS

When prime(n) == 3 (mod 4), then a(n) = A002308(n). - T. D. Noe, Apr 03 2007

STATUS

proposed

editing

#22 by Peter Luschny at Sun Jul 20 16:24:35 EDT 2014

STATUS

editing

proposed

#21 by Peter Luschny at Sun Jul 20 16:24:24 EDT 2014

COMMENTS

When prime(n) == 3 (mod 4), then a(n)=A002308(n). - _T. D. Noe, _, Apr 03 2007

CROSSREFS

Cf. A002308, A048280, A097159.

Cf. A097159

STATUS

proposed

editing

#20 by Michel Marcus at Sun Jul 20 15:44:23 EDT 2014

STATUS

editing

proposed

#19 by Michel Marcus at Sun Jul 20 15:43:44 EDT 2014

REFERENCES

A. A. Bennett, Consecutive quadratic residues, Bull. Amer. Math. Soc., 32 (1926), 283-284.

LINKS

A. A. Bennett, <a href="http://dx.doi.org/10.1090/S0002-9904-1926-04211-7">Consecutive quadratic residues</a>, Bull. Amer. Math. Soc., 32 (1926), 283-284.

MATHEMATICA

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 *)

STATUS

proposed

editing

#18 by Jonathan Sondow at Sun Jul 20 15:32:44 EDT 2014

STATUS

editing

proposed