A002307 - OEIS

A002307

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)

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

1,4

COMMENTS

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

A048280(n) is defined similarly, except that reduced quadratic residues equal to 0 are also included. - Jonathan Sondow, Jul 20 2014

REFERENCES

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).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

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

FORMULA

a(n) <= A048280(n) < 2*sqrt(prime(n)). - Jonathan Sondow, Jul 20 2014

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}] (* Robert G. Wilson v, Jul 28 2004 *)

CROSSREFS

Cf. A002308, A048280, A097159.

Sequence in context: A175470 A098534 A317638 * A287707 A029247 A194020

Adjacent sequences: A002304 A002305 A002306 * A002308 A002309 A002310

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from David W. Wilson

STATUS

approved