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A268397 a(n) is the smallest prime with at least n consecutive primitive roots. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
More terms from Harvey P. Dale, Aug 23 2019
STATUS
approved

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Last modified July 17 22:17 EDT 2024. Contains 374377 sequences. (Running on oeis4.)