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A179678 Primes which are the fifth element of a generalized Wieferich sequence. 0
359, 6211, 13477, 19069, 20431, 22567, 32933, 39041 (list; graph; refs; listen; history; text; internal format)



A generalized Wieferich sequence is an increasing sequence of primes p[1],p[2],... such that a=p[n+1] is a Wieferich prime to base b=p[n], i.e., a^(b-1)=1 (mod b^2).

The present sequence is a subsequence of A179400. The numbers 728437, 1051139, 144 449603 and 5176 948723 found by M. Kamada and D. Broadhurst are also in this sequence. The last two numbers are even 7th elements of a generalized Wieferich sequence, cf. the link.


Table of n, a(n) for n=1..8.

D. Broadhurst, Re: 1993/2011 puzzle [and Puzzle 7], in primenumbers@yahoogroups.com, Jan 2011.


The smallest generalized Wieferich sequence of length 5 is (3, 11, 71, 331, 359): 3^10=1 (mod 11^2), 11^70=1 (mod 71^2), 71^330=1 (mod 331^2) and 331^358=1 (mod 359^2). Therefore, a(1)=359.

It happens that after a(2)=6211, there are four subsequent elements of A179400, namely 13477, 19069, 20431 and 22567, which are also member of a sequence of length 5 and thus in this sequence.


(PARI) fp(p)={ my(a=precprime(p)); while(Mod(a, p^2)^(p-1)-1 & a=precprime(a-1), ); a }

forprime(p=1, default(primelimit), a=p; for(c=1, 4, (a=fp(a))|next(2)); print1(p", "))


Sequence in context: A142852 A158307 A013325 * A101996 A237017 A097570

Adjacent sequences:  A179675 A179676 A179677 * A179679 A179680 A179681




M. F. Hasler, Jan 10 2011



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Last modified December 19 11:13 EST 2018. Contains 318246 sequences. (Running on oeis4.)