A255885 Smallest base b such that there exist exactly n Wieferich pseudoprimes (composites c satisfying b^(c-1) == 1 (mod c^2)) less than b.

17, 65, 145, 485, 649, 1297, 577, 2024, 5185, 8182, 7057, 8749, 14401, 30753, 56449, 57601, 77401, 129473, 51841, 129601, 254017, 296449, 202501, 389377

Offset: 1

Author

Felix Fröhlich, Mar 09 2015

Keywords

• nonn
• more

Crossrefs

Cf. A244752, A252232, A255901.

Programs

PARI

for(n=1, 10, b=2; while(b > 0, i=0; forcomposite(c=2, b, if(Mod(b, c^2)^(c-1)==1, i++)); if(i==n, print1(b, ", "); break({1})); b++))

Python

from itertools import count
from sympy import isprime
def A255885(n):
    for b in count(1):
        if n == sum(1 for c in range(2,b+1) if not isprime(c) and pow(b,c-1,c**2) == 1):
            return b # Chai Wah Wu, May 18 2022

Extensions

a(20) from Chai Wah Wu, May 18 2022

a(21)-a(24) from Chai Wah Wu, May 19 2022