

A275338


Smallest prime p where a base b with 1 < b < p exists such that b^(p1) == 1 (mod p^n).


0




OFFSET

1,1


COMMENTS

Smallest prime p such that A254444(i) >= n, where i is the index of p in A000040.
For n > 1, a(n) is a term of A134307.
For n > 1, if A000040(i) is a term of the sequence, then A249275(i) < A000040(i).
For n > 1, smallest prime p such that T(n, i) < p, where i is the index of p in A000040 and T = A257833.
a(4) > 5*10^8 if it exists (see Fischer link).


LINKS

Table of n, a(n) for n=1..3.
R. Fischer, Thema: Fermatquotient B^(P1) == 1 (mod P^3).


EXAMPLE

For n = 3: p = 113 satisfies 68^(p1) == 1 (mod p^3) and there is no smaller prime p such that p satisfies b^(p1) == 1 (mod p^3) for some b with 1 < b < p, so a(3) = 113.


PROG

(PARI) a(n) = forprime(p=1, , for(b=2, p1, if(Mod(b, p^n)^(p1)==1, return(p))))


CROSSREFS

Cf. A134307, A254444, A257833.
Sequence in context: A183381 A136985 A131546 * A068693 A036930 A198085
Adjacent sequences: A275335 A275336 A275337 * A275339 A275340 A275341


KEYWORD

nonn,hard,more,bref


AUTHOR

Felix FrÃ¶hlich, Jul 28 2016


STATUS

approved



