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A297846
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Primes p such that p is the largest member of a Wieferich tuple.
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11
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71, 359, 487, 863, 1069, 1093, 1483, 1549, 2281, 3511, 4871, 6451, 6733, 7393, 12049, 13691, 14107, 14149, 15377, 17401, 18787, 20771, 29573, 32933, 35747, 39233, 44483, 46021, 48947, 49559, 54787, 54979, 59197, 60493, 69401, 69653, 77263, 77867, 105323, 122327
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OFFSET
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1,1
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COMMENTS
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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:
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).
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LINKS
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EXAMPLE
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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.
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PROG
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(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)
newprimes(v, w) = setminus(w, v)
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))
forprime(p=1, , if(is(p), print1(p, ", ")))
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CROSSREFS
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Supersequence of column 1 of A271100.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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