A275338 Smallest prime p where a base b with 1 < b < p exists such that b^(p-1) == 1 (mod p^n).

3, 11, 113

Offset: 1

Author

Felix Fröhlich, Jul 28 2016

Keywords

• nonn
• hard
• more
• bref

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).

Examples

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

Links

• R. Fischer, Thema: Fermatquotient B^(P-1) == 1 (mod P^3).

Crossrefs

Cf. A134307, A254444, A257833.

Programs

PARI

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