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A297846 Primes p such that p is the largest member of a Wieferich tuple. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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).

LINKS

Table of n, a(n) for n=1..40.

EXAMPLE

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.

PROG

(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, ", ")))

CROSSREFS

Supersequence of A253683, A266829 and A289899.

Supersequence of column 1 of A271100.

Sequence in context: A142375 A215470 A344282 * A142304 A201313 A078949

Adjacent sequences:  A297843 A297844 A297845 * A297847 A297848 A297849

KEYWORD

nonn

AUTHOR

Felix Fröhlich, Jan 07 2018

EXTENSIONS

More terms from Felix Fröhlich, Jan 22 2018

STATUS

approved

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Last modified June 15 18:33 EDT 2021. Contains 345049 sequences. (Running on oeis4.)