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.

A070180 Primes p such that x^3 = 2 has a solution mod p, but x^(3^2) = 2 has no solution mod p.

Original entry on oeis.org

109, 307, 433, 739, 811, 919, 1423, 1459, 1999, 2017, 2143, 2179, 2251, 2287, 2341, 2791, 2917, 2953, 3061, 3259, 3331, 3457, 3889, 4177, 4339, 4519, 4663, 5113, 5167, 5419, 5437, 5653, 6301, 6427, 6661, 6679, 6967, 7723, 7741, 8011, 8389, 8713
Offset: 1

Views

Author

Klaus Brockhaus, Apr 29 2002

Keywords

Crossrefs

Cf. A040028, A049596, A059262, A059667, A070179, A070181 - A070188.

Programs

  • Magma
    [p: p in PrimesUpTo(10000) | not exists{x: x in ResidueClassRing(p) | x^9 eq 2} and exists{x: x in ResidueClassRing(p) | x^3 eq 2}]; // Vincenzo Librandi, Sep 21 2012
  • PARI
    forprime(p=2,8800,x=0; while(x
  • PARI
    ok(p, r, k1, k2)={
    if (  Mod(r,p)^((p-1)/gcd(k1,p-1))!=1, return(0) );
    if (  Mod(r,p)^((p-1)/gcd(k2,p-1))==1, return(0) );
    return(1);
}
forprime(p=2,10^4, if (ok(p,2,3,3^2),print1(p,", ")));
/* Joerg Arndt, Sep 21 2012 */

A070183 Primes p such that x^6 = 2 has a solution mod p, but x^(6^2) = 2 has no solution mod p.

Original entry on oeis.org

17, 41, 137, 401, 433, 449, 457, 521, 569, 641, 761, 809, 857, 919, 929, 953, 977, 1361, 1409, 1423, 1657, 1697, 1999, 2017, 2081, 2143, 2153, 2287, 2297, 2417, 2609, 2633, 2729, 2753, 2777, 2791, 2801, 2897, 2953, 3041, 3209, 3329, 3457, 3593, 3617
Offset: 1

Views

Author

Klaus Brockhaus, Apr 29 2002

Keywords

Links

Crossrefs

Cf. A040992, A049568, A059264, A059667, A070179, A070180, A070181, A070182, A070184, A070185, A070186, A070187, A070188.

Programs

  • Magma
    [p: p in PrimesUpTo(5000) | not exists{x: x in ResidueClassRing(p) | x^36 eq 2} and exists{x: x in ResidueClassRing(p) | x^6 eq 2}]; // Vincenzo Librandi, Sep 21 2012
  • Maple
    select(p -> isprime(p) and [msolve(x^6=2,p)]<>[] and [msolve(x^36=2,p)]=[] , [seq(i,i=3..10^4,2)]); # Robert Israel, May 13 2018
  • PARI
    forprime(p=2,3700,x=0; while(x
  • PARI
    ok(p, r, k1, k2)={
    if (  Mod(r,p)^((p-1)/gcd(k1,p-1))!=1, return(0) );
    if (  Mod(r,p)^((p-1)/gcd(k2,p-1))==1, return(0) );
    return(1);
}
forprime(p=2,10^4, if (ok(p,2,6,6^2),print1(p,", ")));
/* Joerg Arndt, Sep 21 2012 */
  • Python
    from itertools import count, islice
from sympy import nextprime, is_nthpow_residue
def A070183_gen(startvalue=2): # generator of terms >= startvalue
    p = max(nextprime(startvalue-1),2)
    while True:
        if is_nthpow_residue(2,6,p) and not is_nthpow_residue(2,36,p):
            yield p
        p = nextprime(p)
A070183_list = list(islice(A070183_gen(),20)) # Chai Wah Wu, May 02 2024

A070182 Primes p such that x^5 = 2 has a solution mod p, but x^(5^2) = 2 has no solution mod p.

Original entry on oeis.org

151, 251, 3251, 3301, 4751, 8501, 11251, 11701, 13751, 14251, 14951, 15551, 16451, 17401, 18401, 21401, 21601, 24251, 28351, 28901, 32251, 32401, 32801, 34301, 36151, 36451, 37201, 40351, 42451, 42701, 44201, 45751, 46051, 46451, 46901
Offset: 1

Views

Author

Klaus Brockhaus, Apr 29 2002

Keywords

Crossrefs

Cf. A040159, A049557, A059313, A059667, A070179 - A070181, A070183 - A070188.

Programs

  • Magma
    [p: p in PrimesUpTo(50000) | not exists{x: x in ResidueClassRing(p) | x^25 eq 2} and exists{x: x in ResidueClassRing(p) | x^5 eq 2}]; // Vincenzo Librandi, Sep 21 2012
  • PARI
    forprime(p=2,47000,x=0; while(x
  • PARI
    ok(p, r, k1, k2)={
    if (  Mod(r,p)^((p-1)/gcd(k1,p-1))!=1, return(0) );
    if (  Mod(r,p)^((p-1)/gcd(k2,p-1))==1, return(0) );
    return(1);
}
forprime(p=2,10^5, if (ok(p,2,5,5^2),print1(p,", ")));
/* Joerg Arndt, Sep 21 2012 */
Showing 1-3 of 3 results.

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

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