
OFFSET

1,1


COMMENTS

A Wieferich cycle is a repeating cycle in the trajectory of p under successive applications of the map p > A039951(p), i.e., a part of a row of A288097 repeating indefinitely.
The above cycles could more precisely be called "order1 Wieferich cycles". A cycle in a row of A281002 could be called an "order2 Wieferich cycle".
The cycles corresponding to a(1)a(3) are {3, 11, 71}, {2, 1093} and {83, 4871}, respectively.
The order of the cycle is not to be confused with its length. The order1 cycle {3, 11, 71} is a cycle of length 3, while the order1 cycles {2, 1093} and {83, 4871} are cycles of length 2.
Wieferich cycles are special cases of Wieferich tuples (cf. A271100).
a(4) > 20033669 if it exists.


LINKS

Table of n, a(n) for n=1..3.


EXAMPLE

71 is a term, since A039951(71) = 3, A039951(3) = 11 and A039951(11) = 71, so {3, 11, 71} is a Wieferich cycle of length 3 and 71 is the largest member of that cycle.


PROG

(PARI) leastwieferich(base, bound) = forprime(p=1, bound, if(Mod(base, p^2)^(p1)==1, return(p))); 0
is(n) = my(v=[leastwieferich(n, n)]); while(1, if(v[#v]==0, return(0), v=concat(v, leastwieferich(v[#v], n))); my(x=#v1); while(x > 1, if(v[#v]==v[x], if(n==vecmax(v), return(1), return(0))); x))
forprime(p=1, , if(is(p), print1(p, ", ")))


CROSSREFS

Cf. A039951, A252801, A252802, A252812, A268479, A269111, A271100, A281002, A288097.
Sequence in context: A175215 A231414 A071827 * A267475 A241940 A254872
Adjacent sequences: A289896 A289897 A289898 * A289900 A289901 A289902


KEYWORD

nonn,hard,bref,more


AUTHOR

Felix FrÃ¶hlich, Jul 14 2017


STATUS

approved

