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.

A205534 Record values of A205531 and A205535.

Original entry on oeis.org

1, 3, 5, 6, 9, 11, 15, 17, 21, 27, 29, 35, 39, 45, 51
Offset: 1

Views

Author

M. F. Hasler, Jan 28 2012

Keywords

Comments

Related to the 4.X Selfridge Conjecture by P. Underwood, cf. link.
Records occur at [p=A205532(n), y=A205534(n)] = [2, 1], [13, 3], [61, 5], [109, 6], [1009, 9], [2689, 11], [8089, 15], [33049, 17], [53881, 21], [87481, 27], [483289, 29], [515761, 35], [1083289, 39], [3818929, 45], [9257329, 51],...
It appears that all records > 6 occur at elements of A102295.

Links

Programs

  • PARI
    m=-1;forprime(p=1,default(primelimit),if(m+0A205535(p),m), print1(m",")))

A205531 Least nonnegative integer y such that Kronecker(y^2 - 4, p(n)) == -1 and (x+2)^(p(n)+1) == 5 -+ 2*y (mod p(n), mod x^2 +- y*x + 1).

Original entry on oeis.org

1, 0, 1, 0, 0, 3, 1, 0, 0, 1, 0, 3, 1, 0, 0, 1, 0, 5, 0, 0, 3, 0, 0, 1, 3, 1, 0, 0, 6, 1, 0, 0, 1, 0, 1, 0, 3, 0, 0, 1, 0, 5, 0, 3, 1, 0, 0, 0, 0, 5, 1, 0, 5, 0, 1, 0, 1, 0, 3, 1, 0, 1, 0, 0, 3, 1, 0, 3, 0, 5, 1, 0, 0, 3, 0, 0, 1, 3, 1, 5, 0, 6, 0, 3, 0, 0, 1, 3, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 6, 0, 1, 0, 1, 0, 3, 0, 1, 0, 5, 0, 3, 1, 0, 0, 1, 0, 0, 1, 0, 5, 3, 1, 0, 0, 1, 6, 0, 0, 3, 0, 0
Offset: 1

Views

Author

M. F. Hasler, Jan 28 2012

Keywords

Comments

Related to the 4.X Selfridge Conjecture by P. Underwood, which states that p is prime iff such a y exists.
Records occur at [p=prime(k),y=a(k)] = [A205532(n), A205534(n)] = [2, 1], [13, 3], [61, 5], [109, 6], [1009, 9], [2689, 11], [8089, 15], [33049, 17], [53881, 21], [87481, 27], [483289, 29], [515761, 35], [1083289, 39], [3818929, 45], ...

Links

Programs

A205526 Least positive integer y such that Kronecker(y^2 - 4, p(n)) == -1 and (x+2)^(p(n)+1) == 5 -+ 2*y (mod p(n), mod x^2 +- y*x + 1).

Original entry on oeis.org

1, 3, 1, 3, 1, 3, 1, 4, 1, 1, 4, 3, 1, 3, 1, 1, 1, 5, 3, 1, 3, 4, 1, 1, 3, 1, 3, 1, 6, 1, 3, 1, 1, 4, 1, 4, 3, 3, 1, 1, 1, 5, 1, 3, 1, 4, 4, 3, 1, 5, 1, 1, 5, 1, 1, 1, 1, 4, 3, 1, 3, 1, 3, 1, 3, 1, 4, 3, 1, 5, 1, 1, 3, 3, 4, 1, 1, 3, 1, 5, 1, 6, 1, 3, 4, 1, 1, 3, 1, 3, 1, 1, 3, 1, 4, 1, 1, 1, 3, 6, 3, 1, 1, 1, 4, 3, 1, 1, 1, 5, 3, 3, 1, 4, 4, 1, 3, 1, 1, 1, 5, 3, 1, 1, 4, 1, 6, 1, 3, 3, 4, 1
Offset: 1

Views

Author

M. F. Hasler, Jan 28 2012

Keywords

Comments

This is an alternate version of A205531, which should be considered as the main entry. One has A205526(n)=A205531(n) whenever the latter is nonzero.
Related to the 4.X Selfridge Conjecture by P. Underwood, which states that p is prime iff such an y exists.
Records are [p, y] = [A205532(n), A205534(n)] = [2, 1], [3, 3], [19, 4], [61, 5], [109, 6], [1009, 9], [2689, 11], [8089, 15], [33049, 17], [53881, 21], [87481, 27], [483289, 29], [515761, 35], [1083289, 39], [3818929, 45], ...

Links

Programs

  • PARI
    a(n)={n=prime(n);for(y=1,1e7, kronecker(y^2-4,n)==-1 | next;
Mod(x+Mod(2,n),x^2-y*x+1)^(n+1)==5+2*y | next; Mod(x+Mod(2,n),x^2+y*x+1)^(n+1)==5-2*y & return(y))}
Showing 1-3 of 3 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.