132857

Properties

Appears in sequences

• Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 38.at n=13A031626
• Smallest b > 1 such that the first n primes p (i.e., A000040(1)-A000040(n)) all satisfy b^(p-1) == 1 (mod p^2), i.e., smallest base b larger than 1 such that any member of the set of first n primes is a base-b Wieferich prime.at n=5A256236
• Triangle read by rows: T(n, k) = smallest base b > 1 such that p = prime(n) is the k-th base-b Wieferich prime for k = 1, 2, 3, ..., n.at n=20A258787
• Smallest b such that the k consecutive primes starting with prime(n) are all base-b Wieferich primes, i.e., satisfy b^(p-1) == 1 (mod p^2). Square array A(n, k), read by antidiagonals downwards.at n=15A286816
• A(n, k) is the k-th number b > 1 such that b^(prime(n+i)-1) == 1 (mod prime(n+i)^2) for each i = 0..4, with k running over the positive integers; square array, read by antidiagonals, downwards.at n=7A319062
• A(n, k) is the k-th number b > 1 such that b^(prime(n+i)-1) == 1 (mod prime(n+i)^2) for each i = 0..5, with k running over the positive integers; square array, read by antidiagonals, downwards.at n=0A319063
• Bases b where exactly nine primes p with p < b exist such that p is a base-b Wieferich prime.at n=23A325885
• Numbers b > 1 such that the smallest five primes, i.e., 2, 3, 5, 7 and 11 are base-b Wieferich primes.at n=11A339534
• Numbers b > 1 such that the smallest six primes, i.e., 2, 3, 5, 7, 11 and 13 are base-b Wieferich primes.at n=0A339535
• a(n) is the smallest b > 1 such that prime(n), prime(n+1), prime(n+2), prime(n+3), prime(n+4) and prime(n+5) are all base-b Wieferich primes.at n=0A344830
• Prime numbersat n=12401