A268352 Second base-n Wieferich prime, i.e., second smallest prime p such that n^(p-1) == 1 (mod p^2).

3511, 1006003, 3511, 20771, 534851, 491531, 1093, 11, 487

Offset: 2

Author

Felix Fröhlich, Feb 02 2016

Keywords

• nonn
• hard
• more

Comments

Column 2 of table T(n, k) of k-th base-n Wieferich prime for n > 1 (that table is not yet in the OEIS as a sequence).

a(11) is unknown, but must be larger than 1.202*10^13 if it exists (cf. Fischer).

Examples

			a(3) = 1006003, because 1006003 is the second smallest prime p satisfying 3^(p-1) == 1 (mod p^2) (see A014127).
		

Links

• R. Fischer, Thema: Fermatquotient B^(P-1) == 1 (mod P^2)

Crossrefs

Cf. A039951, A178871.

Programs

PARI

a(n) = my(i=0); forprime(p=1, , if(Mod(n, p^2)^(p-1)==1, if(i > 0, return(p), i++)))