OFFSET
1,1
COMMENTS
a(n) is the element in row prime(n), column n of the table in A257833.
Is the sequence always nondecreasing, or stronger, is it always increasing?
For odd primes p, if c is a primitive root mod p^p then b == c^(p^(p-1)) (mod p^p) satisfies this. Thus a(n) < prime(n)^prime(n) for n > 1. - Robert Israel, Jan 30 2017
LINKS
Robert Israel, Table of n, a(n) for n = 1..76
W. Keller and J. Richstein, Solutions of the congruence a^(p-1) == 1 (mod p^r), Math. Comp. 74 (2005), 927-936.
MAPLE
f:= proc(p) local c, j;
c:= numtheory:-primroot(p^p);
min(seq(c &^ (j*p^(p-1)) mod p^p, j=1..p-2))
end proc:
5, seq(f(ithprime(i)), i=2..15); # Robert Israel, Jan 30 2017
MATHEMATICA
Table[b = 2; While[PowerMod[b, (# - 1), #^#] &@ Prime@ n != 1, b++]; b, {n, 4}] (* Michael De Vlieger, Jan 30 2017 *)
PROG
(PARI) a(n) = my(p=prime(n), b=2); while(Mod(b, p^p)^(p-1)!=1, b++); b
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Felix Fröhlich, Jan 29 2017
EXTENSIONS
More terms from Robert Israel, Jan 30 2017
STATUS
approved