|
%I #46 Sep 08 2020 02:16:54
%S 2,11,269,487,653,1093,3511,1006003
%N Primes p that set a new record for the number of bases 1 < b < p for which p is a base-b Wieferich prime.
%C Primes p where A242830(i) reaches record values, where i is the index of p in A000040.
%C The corresponding number of bases are 0, 2, 3, 4, 5, 10, 11, 12. - _Jianing Song_, Feb 07 2019
%C From _Jeppe Stig Nielsen_, Sep 06 2020: (Start)
%C 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.
%C See A334048 for a version where bases b that are powers are not allowed.
%C 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.
%C (End)
%o (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
%Y Cf. A000040, A175932, A242830, A334048.
%Y Subsequence of A175932. Apart from the first term, subsequence of A134307.
%K nonn,hard,more
%O 1,1
%A _Felix Fröhlich_, Mar 07 2015
%E a(1) = 2 inserted by _Jianing Song_, Feb 07 2019
|
