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 1-6 of 6 results.

A355959 Primes p such that (p+2)^(p-1) == 1 (mod p^2).

Original entry on oeis.org

5, 45827
Offset: 1

Views

Author

Felix Fröhlich, Jul 21 2022

Keywords

Comments

a(3) > 107659373057 if it exists.
Primes p such that the Fermat quotient of p base 2 (A007663) is congruent to 1/2 modulo p. - Max Alekseyev, Aug 27 2023

Crossrefs

(p+k)^(p-1) == 1 (mod p^2): A355960 (k=5), A355961 (k=6), A355962 (k=7), A355963 (k=8), A355964 (k=9), A355965 (k=10).
Cf. A007663.

Programs

  • PARI
    forprime(p=1, , if(Mod(p+2, p^2)^(p-1)==1, print1(p, ", ")))

A355960 Primes p such that (p+5)^(p-1) == 1 (mod p^2).

Original entry on oeis.org

3, 23, 1574773
Offset: 1

Views

Author

Felix Fröhlich, Jul 21 2022

Keywords

Comments

Equivalently, primes p such that 5^p == p+5 (mod p^2), or Fermat quotient q_p(5) == 1/5 (mod p). - Max Alekseyev, Sep 16 2024

Crossrefs

(p+k)^(p-1) == 1 (mod p^2): A355959 (k=2), A355961 (k=6), A355962 (k=7), A355963 (k=8), A355964 (k=9), A355965 (k=10).

Programs

  • PARI
    forprime(p=1, , if(Mod(p+5, p^2)^(p-1)==1, print1(p, ", ")))

A355962 Primes p such that (p+7)^(p-1) == 1 (mod p^2).

Original entry on oeis.org

2, 3, 229, 701, 31446553, 1016476523, 8918351831
Offset: 1

Views

Author

Felix Fröhlich, Jul 21 2022

Keywords

Comments

a(8) > 10^13 if it exists. - Jason Yuen, May 12 2024
Equivalently, primes p such that 7^p == p+7 (mod p^2), or Fermat quotient q_p(7) == 1/7 (mod p). - Max Alekseyev, Sep 16 2024

Crossrefs

(p+k)^(p-1) == 1 (mod p^2): A355959 (k=2), A355960 (k=5), A355961 (k=6), A355963 (k=8), A355964 (k=9), A355965 (k=10).

Programs

  • PARI
    forprime(p=1, , if(Mod(p+7, p^2)^(p-1)==1, print1(p, ", ")))

Extensions

a(7) from Jason Yuen, May 12 2024

A355963 Primes p such that (p+8)^(p-1) == 1 (mod p^2).

Original entry on oeis.org

1531, 7445287
Offset: 1

Views

Author

Felix Fröhlich, Jul 21 2022

Keywords

Comments

a(3) > 34294200797 if it exists.

Crossrefs

(p+k)^(p-1) == 1 (mod p^2): A355959 (k=2), A355960 (k=5), A355961 (k=6), A355962 (k=7), A355964 (k=9), A355965 (k=10).

Programs

  • PARI
    forprime(p=1, , if(Mod(p+8, p^2)^(p-1)==1, print1(p, ", ")))

A355964 Primes p such that (p+9)^(p-1) == 1 (mod p^2).

Original entry on oeis.org

13, 19, 2207, 26041, 332698495781
Offset: 1

Views

Author

Felix Fröhlich, Jul 21 2022

Keywords

Comments

a(6) > 10^13 if it exists. - Jason Yuen, May 12 2024

Crossrefs

(p+k)^(p-1) == 1 (mod p^2): A355959 (k=2), A355960 (k=5), A355961 (k=6), A355962 (k=7), A355963 (k=8), A355965 (k=10).

Programs

  • PARI
    forprime(p=1, , if(Mod(p+9, p^2)^(p-1)==1, print1(p, ", ")))

Extensions

a(5) from Jason Yuen, May 12 2024

A355965 Primes p such that (p+10)^(p-1) == 1 (mod p^2).

Original entry on oeis.org

13, 41, 97, 809, 1151, 1657, 800011
Offset: 1

Views

Author

Felix Fröhlich, Jul 21 2022

Keywords

Comments

A computer search taking less than 3 seconds shows there are no further terms below the one millionth prime. - Harvey P. Dale, Mar 04 2024
I ran the PARI program below for 8.5 hours and it did not find any further terms. (I do not know how far it searched.) - N. J. A. Sloane, Mar 05 2024

Crossrefs

(p+k)^(p-1) == 1 (mod p^2): A355959 (k=2), A355960 (k=5), A355961 (k=6), A355962 (k=7), A355963 (k=8), A355964 (k=9).

Programs

  • Mathematica
    Select[Prime[Range[70000]],PowerMod[#+10,#-1,#^2]==1&] (* Harvey P. Dale, Mar 04 2024 *)
  • PARI
    forprime(p=1, , if(Mod(p+10, p^2)^(p-1)==1, print1(p, ", ")))
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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