A353600 Second-smallest Wieferich base of n, i.e., second-smallest b > 1 such that b^(n-1) == 1 (mod n^2).

9, 10, 33, 18, 73, 19, 129, 82, 201, 9, 289, 22, 393, 199, 513, 40, 649, 54, 801, 244, 969, 42, 1153, 443, 1353, 730, 753, 41, 1801, 117, 2049, 604, 2313, 1126, 2593, 76, 2889, 1351, 3201, 148, 3529, 75, 3873, 568, 4233, 67, 4609, 1048, 5001, 2024, 1329, 406

Offset: 2

Author

Felix Fröhlich, Apr 29 2022

Keywords

• nonn

Crossrefs

Cf. A039678, A185103, A256517. Column 2 of A353602.

Programs

PARI

a(n) = my(i=0); for(b=2, oo, if(Mod(b, n^2)^(n-1)==1, if(i==0, i++, return(b))))

Python

def b(n, startk=2):
    k, n2 = startk, n*n
    while pow(k, n-1, n2) != 1: k += 1
    return k
def a(n): return b(n, startk=b(n)+1)
print([a(n) for n in range(2, 54)]) # Michael S. Branicky, Apr 29 2022