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A248865
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Primes p that set a new record for the number of bases 1 < b < p for which p is a base-b Wieferich prime.
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5
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OFFSET
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1,1
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COMMENTS
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Primes p where A242830(i) reaches record values, where i is the index of p in A000040.
The corresponding number of bases are 0, 2, 3, 4, 5, 10, 11, 12. - Jianing Song, Feb 07 2019
From Jeppe Stig Nielsen, Sep 06 2020: (Start)
Note that for a(6) and a(7), all the b values (bases) that are counted are powers of 2; and for a(8) all are powers of 3.
See A334048 for a version where bases b that are powers are not allowed.
One candidate for a(9) is 1645333507; it has 14 bases, the first 13 of which are powers of 5. However, excluding all numbers under 1645333507 as candidates for a(9) may be difficult to do.
(End)
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LINKS
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Table of n, a(n) for n=1..8.
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PROG
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(PARI) my(r=-1); forprime(p=2, , my(b=2, i=0); while(b < p, if(Mod(b, p^2)^(p-1)==1, i++); b++); if(i > r, print1(p, ", "); r=i)) \\ changed to include a(1) = 2 by Jianing Song, Feb 07 2019
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CROSSREFS
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Cf. A000040, A175932, A242830, A334048.
Subsequence of A175932. Apart from the first term, subsequence of A134307.
Sequence in context: A134096 A132571 A102031 * A072386 A185122 A198894
Adjacent sequences: A248862 A248863 A248864 * A248866 A248867 A248868
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KEYWORD
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nonn,hard,more
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AUTHOR
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Felix Fröhlich, Mar 07 2015
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EXTENSIONS
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a(1) = 2 inserted by Jianing Song, Feb 07 2019
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STATUS
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approved
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