cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Jonathan Sondow, Feb 12 2013

Keywords

Examples

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

References

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

Crossrefs

Programs

  • 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]}]