A268397 a(n) is the smallest prime with at least n consecutive primitive roots.

2, 5, 11, 37, 53, 83, 83, 269, 269, 467, 467, 1187, 1559, 1559, 1559, 6803, 6803, 6803, 10559, 10559, 10559, 35279, 38639, 38639, 38639, 38639, 38639

Offset

1,1

Links

Table of n, a(n) for n=1..27.

Example

a(4)=37. 37 has the primitive roots 2, 5, 13, 15, 17, 18, 19, 20, 22, 24, 32, and 35 of which 17, 18, 19, and 20 are consecutive.

Mathematica

PrimRoot[n_] :=Flatten[Position[Table[MultiplicativeOrder[i, n], {i, n - 1}], n - 1]]; t = {}; For[targ = 1, targ <= 22, targ++, flag = 0; For[n = 1, n < 1500, n++, prs = PrimRoot[Prime[n]]; numprs = EulerPhi[Prime[n] - 1]; If[targ > numprs, , For[m = 1, m <= numprs + 1 - targ, m++, temp = Take[prs, {m, m + targ - 1}]; If[temp[[1]] + targ - 1 == temp[[targ]] && flag == 0, t = Append[t, Prime[n]]; flag = 1]; If[flag == 1, Break[]]; ]; If[flag == 1, Break[]]; ]; If[flag == 1, Break[]]; ]]; t
Join[{2}, Module[{prl=Table[{p, Max[Length/@Select[Split[ Differences[ PrimitiveRootList[ p]]], #[[1]]==1&]]}, {p, Prime[Range[1500]]}]}, Table[ SelectFirst[ prl, #[[2]]>=k&], {k, 20}]][[All, 1]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 23 2019 *)

Crossrefs

Cf. A060749, A261438 (has "exactly" instead of "at least").

Sequence in context: A130622 A112600 A156014 * A261438 A092298 A074497

Adjacent sequences: A268394 A268395 A268396 * A268398 A268399 A268400

Keyword

nonn,more

Author

Dimitri Papadopoulos, Feb 03 2016

Extensions

More terms from Harvey P. Dale, Aug 23 2019

Status

approved