A248865 Primes p that set a new record for the number of bases 1 < b < p for which p is a base-b Wieferich prime.

2, 11, 269, 487, 653, 1093, 3511, 1006003

Offset: 1

Author

Felix Fröhlich, Mar 07 2015

Keywords

• nonn
• hard
• more

Comments

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)

Crossrefs

Cf. A000040, A175932, A242830, A334048.

Subsequence of A175932. Apart from the first term, subsequence of A134307.

Programs

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

Extensions

a(1) = 2 inserted by Jianing Song, Feb 07 2019