Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #16 Jun 26 2022 03:08:26
%S 3,15,21,29,34,35,36,36,41
%N a(n) is the number of near-Wieferich primes with |A| <= 10 less than 10^n, where A(k) = A258367(k).
%C A(k) is A258367(k). I believe this was initially defined in Crandall et al. (1997) (in particular pp. 436-437) and it is now common practice for Wieferich searches to report primes with |A| below some predefined limit (for example, the ongoing search at PrimeGrid uses |A| <= 1000).
%H Richard Crandall, Karl Dilcher and Carl Pomerance, <a href="https://doi.org/10.1090/S0025-5718-97-00791-6">A search for Wieferich and Wilson primes</a>, Mathematics of Computation, Vol. 66, No. 217 (1997), pp. 433-449; <a href="http://www.math.dartmouth.edu/~carlp/PDF/paper111.pdf">alternative link</a>.
%H PrimeGrid, <a href="https://www.primegrid.com/stats_ww.php">WW Statistics</a>
%e n | a(n) | A006880(n) | a(n)/A006880(n)*100
%e --------------------------------------------
%e 1 | 3 | 4 | 75.000000
%e 2 | 15 | 25 | 60.000000
%e 3 | 21 | 168 | 12.500000
%e 4 | 29 | 1229 | 2.359642
%e 5 | 34 | 9592 | 0.354462
%e 6 | 35 | 78498 | 0.044587
%e 7 | 36 | 664579 | 0.005417
%e 8 | 36 | 5761455 | 0.000625
%e 9 | 41 | 50847534 | 0.000081
%o (PARI) a258367(n) = abs(centerlift(Mod(2, n^2)^((n-1)/2))\/n) \\ after _Charles R Greathouse IV_ in A258367
%o my(i=0, x=10); forprime(p=3, , if(p > x, print1(i, ", "); x=10*x); if(a258367(p) <= 10, i++))
%Y Cf. A001220, A006880, A195988, A246568, A258367, A353141, A354676, A354677, A354678.
%K nonn,hard,more
%O 1,1
%A _Felix Fröhlich_, Jun 02 2022