A259505 - OEIS

%I #20 Dec 25 2015 03:03:32

%S 997,8647,47521,85991,283411,4594451,5476381,52728733,53920829,

%T 100980223,127072849,436118521,585293099,858905011

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

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

%C a(5) > 276929 if it exists.

%C a(15) > 10^9. - _Hiroaki Yamanouchi_, Dec 19 2015

%e 252^252 = 1 mod 997^2.

%e 5764^5764 = 1 mod 8647^2.

%t 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 *)

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

%Y Cf. A001220, A134307.

%K nonn,hard,more

%O 1,1

%A _Felix Fröhlich_, Nov 08 2015

%E a(5)-a(14) from _Hiroaki Yamanouchi_, Dec 19 2015