A222185 Least prime q with q^(p-1) == 1 (mod p^2), where p = A222184(n).

3, 19, 53, 11, 31, 53, 43, 19, 79, 71, 223, 257, 251, 349, 307, 241, 197, 503, 467, 643, 13, 127, 457, 419, 487, 617, 691, 2, 241, 997, 821, 683, 653, 421, 941, 1069, 1481, 709, 463, 461, 1153, 1381, 631, 449, 1091, 277, 1993, 367, 659, 151, 1657, 823, 1493, 431, 1787, 2063, 1487, 59, 2389, 2131, 479, 1907, 79, 173, 1151, 1831, 419, 1193, 2, 3319

Offset

1,1

References

L. E. Dickson, History of the Theory of Numbers, vol. 1, chap. IV.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Keller and J. Richstein, Fermat quotients that are divisible by p

Example

3 is the smallest prime < A222184(1) = 11 such that 11^2 divides 3^(11-1)-1 = 59048 = 121*488, so a(1) = 3.

Mathematica

L = Select[ Prime[ Range[500]], Product[ PowerMod[ Prime[k], # - 1, #^2] - 1, {k, 1, PrimePi[#] - 1}] == 0 &]; Table[  Min[ Select[ Prime[ Range[ PrimePi[L[[n]]] - 1]], PowerMod[#, L[[n]] - 1, L[[n]]^2] == 1 &]], {n, 1, Length[L]}]

Crossrefs

Cf. A001220, A039678, A134307, A143548, A222184.

Sequence in context: A363697 A239449 A112627 * A265774 A100697 A134268

Adjacent sequences: A222182 A222183 A222184 * A222186 A222187 A222188

Keyword

nonn

Author

Jonathan Sondow, Feb 12 2013

Status

approved