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 A243839 Positive integers n such that prime(n+i) is a primitive root modulo prime(n+j) for any distinct i and j among 0, 1, 2, 3. 4
 8560, 9719, 19228, 20509, 32117, 32352, 44512, 48086, 56967, 63104, 72233, 72538, 73481, 84831, 85736, 87999, 89747, 98220, 102116, 108246, 116228, 123982, 141709, 144344, 147685, 148099, 171214, 173916, 177322, 180836 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS According to the general conjecture in A243837, this sequence should have infinitely many terms. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..50 Hao Pan, Z.-W. Sun, Consecutive primes and Legendre symbols, arXiv preprint arXiv:1406.5951 [math.NT], 2014-2018. EXAMPLE a(1) = 8560 since prime(8560) = 88259, prime(8561) = 88261, and prime(8562) = 88289 are primitive roots modulo prime(8563) = 88301, and 88259, 88261, 88301 are primitive roots modulo 88289, and 88259, 88289, 88301 are primitive roots modulo 88261, and 88261, 88289, 88301 are primitive roots modulo 88259. MATHEMATICA dv[n_]:=Divisors[n] p[n_]:=Prime[n] m=0; Do[Do[If[Mod[p[n]^(Part[dv[p[n+3]-1], i]), p[n+3]]==1||Mod[p[n+1]^(Part[dv[p[n+3]-1], i]),    p[n+3]]==1||Mod[p[n+2]^(Part[dv[p[n+3]-1], i]), p[n+3]]==1, Goto[aa]], {i, 1, Length[dv[p[n+3]-1]]-1}]; Do[If[Mod[p[n]^(Part[dv[p[n+2]-1], i]), p[n+2]]==1||Mod[p[n+1]^(Part[dv[p[n+2]-1], i]),    p[n+2]]==1||Mod[p[n+3]^(Part[dv[p[n+2]-1], i]), p[n+2]]==1, Goto[aa]], {i, 1, Length[dv[p[n+2]-1]]-1}]; Do[If[Mod[p[n]^(Part[dv[p[n+1]-1], i]), p[n+1]]==1||Mod[p[n+2]^(Part[dv[p[n+1]-1], i]),  p[n+1]]==1||Mod[p[n+3]^(Part[dv[p[n+1]-1], i]), p[n+1]]==1, Goto[aa]], {i, 1, Length[dv[p[n+1]-1]]-1}]; Do[If[Mod[p[n+1]^(Part[dv[p[n]-1], i]), p[n]]==1||Mod[p[n+2]^(Part[dv[p[n]-1], i]), p[n]]==1||Mod[p[n+3]^(Part[dv[p[n]-1], i]), p[n]]==1, Goto[aa]], {i, 1, Length[dv[p[n]-1]]-1}]; m=m+1; Print[m, " ", n]; Label[aa]; Continue, {n, 1, 108246}] CROSSREFS Cf. A000040, A243755, A243837. Sequence in context: A297896 A217338 A217163 * A287119 A156846 A324711 Adjacent sequences:  A243836 A243837 A243838 * A243840 A243841 A243842 KEYWORD nonn AUTHOR Zhi-Wei Sun, Jun 12 2014 STATUS approved

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Last modified August 13 05:18 EDT 2022. Contains 356077 sequences. (Running on oeis4.)