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 A002225 a(n) is the smallest prime p such that each of the first n primes has three cube roots mod p. (Formerly M5224 N2274) 5
 31, 307, 643, 5113, 21787, 39199, 360007, 360007, 4775569, 10318249, 10318249, 65139031, 387453811, 913900417, 2278522747, 2741702809, 25147657981 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the smallest prime p == 1 (mod 3) such that each of the first n primes is a cubic residue mod p. - Robert Israel, Aug 02 2016 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). A. E. Western and J. C. P. Miller, Tables of Indices and Primitive Roots. Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968, p. XVI. LINKS A. E. Western and J. C. P. Miller, Tables of Indices and Primitive Roots, Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968 [Annotated scans of selected pages] EXAMPLE For n = 2, the first two primes 2 and 3 each have three cube roots mod 307: 2 has cube roots 52, 270, 292 and 3 has cube roots 192, 194, 228. - Robert Israel, Aug 02 2016 MAPLE Primes:= : pp:= 7: for n from 1 to 12 do   for p from pp by 6 while     not(isprime(p) and andmap(t -> t &^ ((p-1)/3) mod p = 1, Primes))   do od:   A[n]:= p;   pp:= p;   Primes:= [op(Primes), nextprime(Primes[-1])]; od: seq(A[i], i=1..12); # Robert Israel, Aug 02 2016 MATHEMATICA (* This naive program being very slow, limit is set to 8 terms *) lim=8; np[] := While[p=NextPrime[p]; Mod[p, 3]!=1]; crQ[n_, p_] := Reduce[ 0

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Last modified March 23 10:55 EDT 2019. Contains 321424 sequences. (Running on oeis4.)