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

Author

Dimitri Papadopoulos, Feb 03 2016

Keywords

• nonn
• more

Examples

			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.
		

Crossrefs

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

Programs

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 *)

Extensions

More terms from Harvey P. Dale, Aug 23 2019