A002308 Consecutive quadratic nonresidues mod p.

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

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.

Crossrefs

Cf. A002307.

Cf. A129201

Programs

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 *)

Extensions

More terms from David W. Wilson