A097159 Smallest prime p such that there are n consecutive quadratic residues mod p.

2, 7, 11, 19, 43, 67, 83, 131, 283, 277, 467, 479, 1907, 1607, 2543, 1559, 5443, 5711, 6389, 14969, 25703, 10559, 20747, 52057, 136223, 90313, 162263, 18191, 167107, 31391, 376589, 607153, 671947

Offset

1,1

Comments

Additional terms less than 10^6: a(35)=298483, a(36)=422231, a(40)=701399 and a(42)=366791. - T. D. Noe, Apr 03 2007

Links

Table of n, a(n) for n=1..33.

Example

a(22)=10559, a(23)=20747 & a(28)=18191.

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_] := g[n] = f[ JacobiSymbol[ Range[ Prime[n] - 1], Prime[n]], 1][[1]]; g[1] = 1; a = Table[0, {30}]; Do[b = g[n]; If[ a[[b]] < 31 && a[[b]] == 0, a[[b]] = n; Print[b, " = ", Prime[n]]], {n, 2555}]

Crossrefs

Cf. A002307, A097160, A097161.

Cf. A129201.

Sequence in context: A344141 A344142 A338340 * A139603 A141183 A308724

Adjacent sequences: A097156 A097157 A097158 * A097160 A097161 A097162

Keyword

nonn

Author

Robert G. Wilson v, Jul 28 2004

Extensions

More terms from T. D. Noe, Apr 03 2007

Status

approved