

A278611


Bases b > 1 that set a new record for the size of the smallest baseb Wieferich prime.


2




OFFSET

1,1


COMMENTS

Numbers n such that A039951(n) reaches a new record value.
a(1) = 2. Thereafter smallest number x that occurs later in column 1 of A244249 than any y with 1 < y < x.
Let b(n) be the sequence of corresponding smallest Wieferich primes. b(1)b(3) are 1093, 66161 and 46145917691, respectively (cf. A307220).
No term is a perfect power, since then its smallest Wieferich prime is at most the size of the smallest Wieferich prime of the base that is raised to a power.
a(4) is either 47, 72 or 139, depending on which of those bases is the smallest where any Wieferich prime exists. The smallest base139 Wieferich prime is 1822333408543 and any Wieferich primes in bases 47 and 72 are larger than 1.07*10^14 (cf. Fischer).


LINKS

Table of n, a(n) for n=1..3.
R. Fischer, Thema: Fermatquotient B^(P1) == 1 (mod P^2)


EXAMPLE

a(2) = 6, since the smallest base6 Wieferich prime is 66161 and that prime is the second term with a record value in A039951.


PROG

(PARI) smallest_w_prime(n) = forprime(p=1, , if(Mod(n, p^2)^(p1)==1, return(p)))
my(r=0, b=2); while(1, if(smallest_w_prime(b) > r, print1(b, ", "); r=smallest_w_prime(b)); b++)


CROSSREFS

Cf. A039951, A244249, A307220.
Sequence in context: A005161 A062970 A259436 * A088125 A064940 A105142
Adjacent sequences: A278608 A278609 A278610 * A278612 A278613 A278614


KEYWORD

nonn,hard,more,bref


AUTHOR

Felix FrÃ¶hlich, Nov 23 2016


STATUS

approved



