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A259505
Primes p where an integer r with 1 < r < p exists such that r^r == 1 (mod p^2).
0
997, 8647, 47521, 85991, 283411, 4594451, 5476381, 52728733, 53920829, 100980223, 127072849, 436118521, 585293099, 858905011
OFFSET
1,1
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
EXAMPLE
252^252 = 1 mod 997^2.
5764^5764 = 1 mod 8647^2.
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 *)
PROG
(PARI) forprime(p=1, , for(r=2, p-1, if(Mod(r, p^2)^r==1, print1(p, ", "); break({1}))))
CROSSREFS
Sequence in context: A244546 A091365 A235165 * A372046 A317594 A226752
KEYWORD
nonn,hard,more
AUTHOR
Felix Fröhlich, Nov 08 2015
EXTENSIONS
a(5)-a(14) from Hiroaki Yamanouchi, Dec 19 2015
STATUS
approved