A002308 Consecutive quadratic nonresidues mod p. (Formerly M0274 N0097)

0, 1, 2, 2, 3, 4, 3, 4, 4, 3, 4, 4, 5, 5, 4, 6, 5, 6, 6, 6, 4, 6, 7, 6, 6, 5, 7, 6, 10, 4, 7, 8, 5, 5, 6, 7, 5, 6, 6, 5, 6, 6, 6, 5, 5, 6, 7, 7, 7, 6, 7, 6, 5, 7, 6, 7, 9, 7, 7, 7, 9, 5, 7, 10, 7, 7, 8, 7, 8, 6, 8, 8, 9, 5, 8, 8, 5, 8, 9, 7, 8, 12, 6, 7, 10, 8, 9, 9, 7, 8, 11, 12, 8, 8, 10, 8, 7, 6, 10, 10, 9, 7, 10, 9, 7, 6, 9

Offset

1,3

Comments

a(n) is the maximal number of positive reduced quadratic nonresidues which appear consecutively for the n-th prime.

When prime(n) == 3 (mod 4), then a(n) = A002307(n). - T. D. Noe, Apr 03 2007

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.

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]]; g[1] = 0; Table[g[n], {n, 1, 107}] (* Jean-François Alcover, Oct 17 2012, after the Mathematica code of Robert G. Wilson v in A002307 *)

Crossrefs

Cf. A002307.

Cf. A129201

Sequence in context: A014656 A003078 A165359 * A056796 A061295 A081742

Adjacent sequences: A002305 A002306 A002307 * A002309 A002310 A002311

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from David W. Wilson

Status

approved