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

3, 15, 21, 29, 34, 35, 36, 36, 41

Offset: 1

Author

Felix Fröhlich, Jun 02 2022

Keywords

• nonn
• hard
• more

Comments

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).

Examples

			n | a(n) | A006880(n) | a(n)/A006880(n)*100
--------------------------------------------
1 |    3 |          4 | 75.000000
2 |   15 |         25 | 60.000000
3 |   21 |        168 | 12.500000
4 |   29 |       1229 |  2.359642
5 |   34 |       9592 |  0.354462
6 |   35 |      78498 |  0.044587
7 |   36 |     664579 |  0.005417
8 |   36 |    5761455 |  0.000625
9 |   41 |   50847534 |  0.000081
		

Links

• Richard Crandall, Karl Dilcher and Carl Pomerance, A search for Wieferich and Wilson primes, Mathematics of Computation, Vol. 66, No. 217 (1997), pp. 433-449; alternative link.
• PrimeGrid, WW Statistics

Crossrefs

Cf. A001220, A006880, A195988, A246568, A258367, A353141, A354676, A354677, A354678.

Programs

PARI

a258367(n) = abs(centerlift(Mod(2, n^2)^((n-1)/2))\/n) \\ after Charles R Greathouse IV in A258367
my(i=0, x=10); forprime(p=3, , if(p > x, print1(i, ", "); x=10*x); if(a258367(p) <= 10, i++))