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A354675 a(n) is the number of near-Wieferich primes with |A| <= 10 less than 10^n, where A(k) = A258367(k).

%I A354675 #16 Jun 26 2022 03:08:26
%S A354675 3,15,21,29,34,35,36,36,41
%N A354675 a(n) is the number of near-Wieferich primes with |A| <= 10 less than 10^n, where A(k) = A258367(k).
%C A354675 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 A354675 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 A354675 PrimeGrid, <a href="https://www.primegrid.com/stats_ww.php">WW Statistics</a>
%e A354675 n | a(n) | A006880(n) | a(n)/A006880(n)*100
%e A354675 --------------------------------------------
%e A354675 1 |    3 |          4 | 75.000000
%e A354675 2 |   15 |         25 | 60.000000
%e A354675 3 |   21 |        168 | 12.500000
%e A354675 4 |   29 |       1229 |  2.359642
%e A354675 5 |   34 |       9592 |  0.354462
%e A354675 6 |   35 |      78498 |  0.044587
%e A354675 7 |   36 |     664579 |  0.005417
%e A354675 8 |   36 |    5761455 |  0.000625
%e A354675 9 |   41 |   50847534 |  0.000081
%o A354675 (PARI) a258367(n) = abs(centerlift(Mod(2, n^2)^((n-1)/2))\/n) \\ after _Charles R Greathouse IV_ in A258367
%o A354675 my(i=0, x=10); forprime(p=3, , if(p > x, print1(i, ", "); x=10*x); if(a258367(p) <= 10, i++))
%Y A354675 Cf. A001220, A006880, A195988, A246568, A258367, A353141, A354676, A354677, A354678.
%K A354675 nonn,hard,more
%O A354675 1,1
%A A354675 _Felix Fröhlich_, Jun 02 2022