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.

A259502 Primes p such that nextprime(p + 1)^(p - 1) == 1 (mod p^2).

Original entry on oeis.org

5, 47, 151051, 240727, 911135839
Offset: 1

Views

Author

Felix Fröhlich, Nov 08 2015

Keywords

Comments

Nextprime as defined in A007918.
These are Wieferich primes p to a prime base q where the difference between p and q has minimal or almost minimal (if the difference between p and the previous prime is smaller) value.
No further terms up to 10^9.

Crossrefs

Cf. A001220, A007918, A244546, A260377, A260507.

Programs

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

A267487 Primes p such that A001221(p+1)^(p-1) == 1 (mod p^2).

Original entry on oeis.org

2, 3, 7, 31, 127, 1093, 3511, 8191, 131071, 524287
Offset: 1

Views

Author

Felix Fröhlich, Jan 15 2016

Keywords

Comments

No further terms up to 10^9.
Are all terms of A000668 and A001220 in the sequence?
Does the sequence contain any terms not in A000668 or A001220 other than 2?

Crossrefs

Cf. A000668, A001220, A260377.

Programs

  • Maple
    isA267487 := proc(p)
    if isprime(p) then
        A001221(p+1) ;
        simplify(modp(% &^ (p-1),p^2) =1 );
    else
        false;
    end if;
end proc:
p := 2;
for i from 1 do
    if isA267487(p) then
        printf("%d\n",p) ;
    end if;
    p := nextprime(p) ;
end do: # R. J. Mathar, Jan 23 2016
  • Mathematica
    Select[Prime[Range[3200]], Mod[PrimeNu[# + 1], #^2]^(# - 1) == 1 &] (* G. C. Greubel, Apr 25 2017 *)
  • PARI
    forprime(p=1, 1e9, if(Mod(omega(p+1), p^2)^(p-1)==1, print1(p, ", ")))

A306909 Primes p such that Omega(p + 1)^(p - 1) == 1 (mod p^2), where Omega is A001222.

Original entry on oeis.org

2, 11, 1093, 3511, 20771, 534851, 1006003, 3152573
Offset: 1

Views

Author

Felix Fröhlich, Mar 16 2019

Keywords

Comments

a(9) > 807795277 if it exists.
a(9) > 3.5*10^12 if it exists. - Giovanni Resta, Apr 09 2019

Examples

			A001222(20772) = 5 and 5^(20771-1) == 1 (mod 20771^2), so 20771 is a term of the sequence.

Crossrefs

Cf. A001220, A001222, A260377, A267487.

Programs

  • Mathematica
    Select[Prime@ Range@ 230000, PowerMod[ PrimeOmega[# + 1], #-1, #^2] == 1 &] (* Giovanni Resta, Apr 09 2019 *)
  • PARI
    forprime(p=1, , if(Mod(bigomega(p+1), p^2)^(p-1)==1, print1(p, ", ")))
Showing 1-3 of 3 results.

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

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