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%I #8 Jan 22 2018 10:59:27
%S 71,359,487,863,1069,1093,1483,1549,2281,3511,4871,6451,6733,7393,
%T 12049,13691,14107,14149,15377,17401,18787,20771,29573,32933,35747,
%U 39233,44483,46021,48947,49559,54787,54979,59197,60493,69401,69653,77263,77867,105323,122327
%N Primes p such that p is the largest member of a Wieferich tuple.
%C Let p_1, p_2, p_3, ..., p_u be a set P of distinct prime numbers and let m_1, m_2, m_3, ..., m_u be a set V of variables. Then P is a Wieferich u-tuple if there exists a mapping from the elements of P to the elements of V such that each of the following congruences is satisfied:
%C m_1^(m_2-1) == 1 (mod (m_2)^2), m_2^(m_3-1) == 1 (mod (m_3)^2), ..., m_u^(m_1-1) == 1 (mod (m_1)^2).
%e The primes 31, 79, 251, 263, 421 and 1483 satisfy 31^(79-1) == 1 (mod 79^2), 79^(263-1) == 1 (mod 263^2), 263^(251-1) == 1 (mod 251^2), 251^(421-1) == 1 (mod 421^2), 421^(1483-1) == 1 (mod 1483^2) and 1483^(31-1) == 1 (mod 31^2), so those primes form a Wieferich tuple. Since 1483 is the largest member of the tuple, 1483 is a term of the sequence.
%o (PARI) findwiefs(vec, lim) = my(v=[]); for(k=1, #vec, forprime(p=1, lim, if(Mod(vec[k], p^2)^(p-1)==1, v=concat(v, [p])))); vecsort(v, , 8)
%o newprimes(v, w) = setminus(w, v)
%o is(n) = my(v=findwiefs([n], n), w=[], np=[]); while(1, w=findwiefs(v, n); if(newprimes(v, w)==[], return(0), if(setsearch(vecsort(newprimes(v, w)), n) > 0, return(1))); v=concat(v, newprimes(v, w)); v=vecsort(v, , 8))
%o forprime(p=1, , if(is(p), print1(p, ", ")))
%Y Supersequence of A253683, A266829 and A289899.
%Y Supersequence of column 1 of A271100.
%K nonn
%O 1,1
%A _Felix Fröhlich_, Jan 07 2018
%E More terms from _Felix Fröhlich_, Jan 22 2018
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