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 A222206 Least prime p such that q^(p-1) == 1 (mod p^2) for n primes q < p. 2
 2, 11, 349, 13691, 24329 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS I found no new terms < 5*10^6. - J. Stauduhar, Mar 23 2013 a(5) > 13*10^6, if it exists. Note that, up to 13*10^6, the only other prime p (apart 24329) such that the congruence is satisfied for 4 primes q < p is 9656869. - Giovanni Resta, May 23 2017 REFERENCES L. E. Dickson, History of the Theory of Numbers, vol. 1, chap. IV. LINKS W. Keller and J. Richstein, Fermat quotients that are divisible by p. [Broken link] Wilfrid Keller and Jörg Richstein, Solutions of the congruence a^(p-1) == 1 (mod (p^r)), Math. Comp. 74 (2005), 927-936. EXAMPLE For the prime p = 349, but for no smaller prime, there are 2 primes q = 223 and 317 < p with  q^(p-1) == 1 (mod p^2), so a(2) = 349. MATHEMATICA f[n_] := Block[{p = 2, q = {}}, While[ Count[ PowerMod[ q, p - 1, p^2], 1] != n, q = Join[q, {p}]; p = NextPrime@ p]; p]; Array[f, 5, 0] (* Robert G. Wilson v, Mar 09 2015 *) PROG (PARI) a(n) = {nb = 0; p = 2; while (nb != n, p = nextprime(p+1); nb = 0; forprime(q=2, p-1, if (Mod(q, p^2)^(p-1) == 1, nb ++); if (nb > n, break); ); ); p; } \\ Michel Marcus, Mar 08 2015 CROSSREFS Cf. A001220, A039678, A134307, A143548, A222184, A222185. Sequence in context: A072386 A185122 A198894 * A229268 A309068 A015180 Adjacent sequences:  A222203 A222204 A222205 * A222207 A222208 A222209 KEYWORD nonn,more AUTHOR Jonathan Sondow, Feb 12 2013 STATUS approved

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Last modified May 25 17:53 EDT 2020. Contains 334595 sequences. (Running on oeis4.)