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.

User: Thomas Bokk

Thomas Bokk's wiki page.

Thomas Bokk has authored 4 sequences.

A257642 Positive integers N such that there is a triangle with rational sides having area and perimeter both equal N.

Original entry on oeis.org

21, 24, 26, 27, 28, 30, 31, 33, 35, 36, 37, 39, 42, 43, 45, 47, 50, 51, 52, 55, 56, 58, 60, 61, 62, 63, 64, 66, 67, 71, 74, 75, 76, 77, 79, 81, 83, 85, 86, 88, 90, 91, 93, 94, 95, 96, 98, 99, 100, 102, 103, 105, 106, 107, 108, 109, 110, 112, 113, 115, 116, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 137, 138, 141, 143, 145, 147, 148, 149, 150
Offset: 1

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Author

Thomas Bokk, Nov 05 2015

Keywords

Comments

A positive integer N is in the sequence if and only if there exist positive rational numbers x,y such that x*y>1 and 4*x*y*(x+y)/(x*y-1)=N.
Except for N=27, a positive integer N is in this sequence if and only if N>20 and the elliptic curve w^2 = u^3 + N^2*(u+64)^2 has positive rank.

Crossrefs

Cf. A135412, A206334, A228914, A117319, A228380.

A253881 Positive integers N such that rational Diophantine triple {-1/N, N, (N^2-1)/N} can be extended to a quadruple.

Original entry on oeis.org

9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 29, 31, 33, 34, 37, 40, 41, 43, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 60, 61, 62, 65, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 83, 84, 85, 86, 88, 91, 93, 95, 96, 97, 99, 103, 105, 106, 111, 113, 114, 115, 117, 119
Offset: 1

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Author

Thomas Bokk, Jan 17 2015

Keywords

Comments

Positive integer N belongs to this sequence if and only if the elliptic curve y^2 = x^3 + (N^2+1/N^2)*x^2 + x has positive rank.

A228914 Positive integers N such that 1/N = p/q - q/p + r/s - s/r for some positive integers p,q,r,s.

Original entry on oeis.org

4, 5, 9, 12, 15, 20, 21, 22, 24, 26, 29, 30, 31, 32, 34, 35, 36, 37, 38, 40, 43, 44, 53, 55, 56, 58, 59, 60, 62, 64, 66, 67, 68, 69, 70, 71, 74, 76, 77, 80, 82, 84, 86, 87, 88, 90, 91, 92, 94, 95, 102, 103, 104, 105, 106, 108, 109, 110, 112, 113, 115, 117, 122, 123, 129, 131, 132, 133, 135, 136, 137, 138, 139, 140, 141, 143, 144, 147
Offset: 1

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Author

Thomas Bokk, Sep 13 2013

Keywords

Comments

Positive integer N belongs to this sequence if and only if the elliptic curve y^2 = x^3 + (8*N^2+1)*x^2 + 16*N^4*x has positive rank.

Crossrefs

Cf. A206334, A228380

Programs

  • PARI
    { isA228914(n) = ellanalyticrank(ellinit([0, 8*n^2+1, 0, 16*n^4, 0]))[1]; } /* Max Alekseyev, Dec 30 2015 */

Extensions

More terms from Max Alekseyev, Sep 13 2013

A228380 Positive integers N such that N = (p^2+q^2)*(r^2-s^2)/((p^2-q^2)*(r^2+s^2)) for some positive integers p,q,r,s.

Original entry on oeis.org

1, 6, 13, 16, 18, 22, 23, 32, 33, 35, 36, 37, 41, 42, 43, 44, 45, 46, 50, 51, 53, 57, 58, 59, 60, 61, 63, 67, 69, 70, 74, 75, 77, 78, 79, 80, 83, 84, 85, 86, 88, 89, 90, 93, 94, 95, 96, 97, 98, 102, 104, 110, 112, 116, 117, 118, 119, 122, 123, 124, 126, 128, 132, 133, 134, 137, 138, 141, 142, 143, 152
Offset: 1

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Author

Thomas Bokk, Aug 21 2013

Keywords

Comments

Integer N>1 belongs to this sequence if and only if the elliptic curve y^2 = x^3 - (N^2+1)*x^2 + N^2*x has positive rank.

Crossrefs

Cf. A117319

Programs

  • PARI
    { isA228380(n) = ellanalyticrank(ellinit([0,-(n^2+1),0,n^2,0]))[1]; } /* Max Alekseyev, Sep 29 2015 */

Extensions

More terms from Max Alekseyev, Sep 29 2015

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