A259505 Primes p where an integer r with 1 < r < p exists such that r^r == 1 (mod p^2).

997, 8647, 47521, 85991, 283411, 4594451, 5476381, 52728733, 53920829, 100980223, 127072849, 436118521, 585293099, 858905011

Offset: 1

Author

Felix Fröhlich, Nov 08 2015

Keywords

• nonn
• hard
• more

Comments

Inspired by the Nov 28 2014 comment from Thomas Ordowski in A001220.

a(5) > 276929 if it exists.

a(15) > 10^9. - Hiroaki Yamanouchi, Dec 19 2015

Examples

			252^252 = 1 mod 997^2.
5764^5764 = 1 mod 8647^2.
		

Crossrefs

Cf. A001220, A134307.

Programs

Mathematica

p = 2; lst = {}; While[p < 100001, r = 2; While[r < p, If[ PowerMod[r, r, p^2] == 1, AppendTo[lst, p]]; r++]; p = NextPrime@ p] (* Robert G. Wilson v, Dec 06 2015 *)

PARI

forprime(p=1, , for(r=2, p-1, if(Mod(r, p^2)^r==1, print1(p, ", "); break({1}))))

Extensions

a(5)-a(14) from Hiroaki Yamanouchi, Dec 19 2015