cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

3, 15, 21, 29, 34, 35, 36, 36, 41
Offset: 1

Views

Author

Felix Fröhlich, Jun 02 2022

Keywords

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

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++))

A354676 a(n) = number of near-Wieferich primes with |A| <= 100 less than 10^n.

Original entry on oeis.org

3, 24, 105, 154, 213, 243, 268, 288, 307
Offset: 1

Views

Author

Felix Fröhlich, Jun 02 2022

Keywords

Comments

n | a(n) | A006880(n) | a(n)/A006880(n)*100
--------------------------------------------
1 | 3 | 4 | 75.000000
2 | 24 | 25 | 96.000000
3 | 105 | 168 | 62.500000
4 | 154 | 1229 | 12.530512
5 | 213 | 9592 | 2.220600
6 | 243 | 78498 | 0.309562
7 | 268 | 664579 | 0.040326
8 | 288 | 5761455 | 0.004998
9 | 307 | 50847534 | 0.000603

Crossrefs

Cf. A006880, A195988, A246568, A258367, A353141, A354675, 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) <= 100, i++))

A354677 a(n) = number of near-Wieferich primes with |A| <= 1000 less than 10^n.

Original entry on oeis.org

3, 24, 167, 698, 1155, 1502, 1812, 2064, 2297
Offset: 1

Views

Author

Felix Fröhlich, Jun 02 2022

Keywords

Comments

n | a(n) | A006880(n) | a(n)/A006880(n)*100
--------------------------------------------
1 | 3 | 4 | 75.000000
2 | 24 | 25 | 96.000000
3 | 167 | 168 | 99.404761
4 | 698 | 1229 | 56.794141
5 | 1155 | 9592 | 12.041284
6 | 1502 | 78498 | 1.913424
7 | 1812 | 664579 | 0.272653
8 | 2064 | 5761455 | 0.035824
9 | 2297 | 50847534 | 0.004517

Crossrefs

Cf. A006880, A195988, A246568, A258367, A353141, A354675, A354676, 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) <= 1000, i++))
Showing 1-3 of 3 results.

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