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.

Previous Showing 21-22 of 22 results.

A065908 Second solution mod p of x^4 = 2 for primes p such that only two solutions exist.

Original entry on oeis.org

5, 15, 16, 30, 56, 76, 55, 123, 135, 133, 158, 152, 125, 147, 195, 208, 197, 281, 214, 226, 324, 403, 307, 364, 401, 445, 377, 310, 574, 641, 701, 492, 677, 609, 602, 444, 636, 854, 791, 511, 599, 852, 690, 623, 786, 914, 769, 698, 692, 1102, 1201, 1073
Offset: 1

Views

Author

Klaus Brockhaus, Nov 29 2001

Keywords

Comments

Conjecture: no integer occurs more than three times in this sequence. Confirmed for the first 2399 terms of A007522 (primes < 100000). In this section, there are no integers which do occur thrice.

Examples

			a(3) = 16, since 31 is the third term of A007522 and 16 is the second solution mod 31 of x^4 = 2.

Crossrefs

A040098, A007522, A065907.

Programs

  • PARI
    a065908(m) = local(s); forprime(p = 2,m,s = []; for(x = 0,p-1, if(x^4%p == 2%p,s = concat(s,[x]))); if(matsize(s)[2] == 2,print1(s[2],",")))
a065908(1400)

Formula

a(n) = second (largest) solution mod p of x^4 = 2, where p is the n-th prime such that x^4 = 2 has only two solutions mod p, i.e. p is the n-th term of A007522.

A070181 Primes p such that x^4 = 2 has a solution mod p, but x^(4^2) = 2 has no solution mod p.

Original entry on oeis.org

113, 281, 353, 577, 593, 617, 1033, 1049, 1097, 1153, 1193, 1201, 1217, 1249, 1481, 1553, 1601, 1753, 1777, 1889, 2129, 2273, 2281, 2393, 2473, 2689, 2833, 2857, 3049, 3089, 3121, 3137, 3217, 3313, 3361, 3529, 3673, 3761, 3833, 4001, 4049, 4153, 4217
Offset: 1

Views

Author

Klaus Brockhaus, Apr 29 2002

Keywords

Crossrefs

Cf. A040098, A045315, A045316, A059667, A070179, A070180, A070182 - A070188.

Programs

  • Magma
    [p: p in PrimesUpTo(5000) | not exists{x: x in ResidueClassRing(p) | x^16 eq 2} and exists{x: x in ResidueClassRing(p) | x^4 eq 2}]; // Vincenzo Librandi, Sep 21 2012
  • PARI
    forprime(p=2,4250,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,2,4,4^2),print1(p,", ")));
/* Joerg Arndt, Sep 21 2012 */
Previous Showing 21-22 of 22 results.

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

Content is available under The OEIS End-User License Agreement.