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 1-5 of 5 results.

A094136 Values x of smallest positive pair (x,y) satisfying x^2 - 2*y^2 = -+d, where d=A058529(n).

Original entry on oeis.org

1, 1, 1, 5, 1, 3, 7, 1, 1, 9, 9, 3, 1, 5, 11, 3, 1, 5, 13, 1, 13, 3, 7, 1, 5, 15, 3, 7, 1, 17, 5, 17, 17, 1, 7, 9, 5, 3, 1, 7, 19, 19, 5, 3, 1, 7, 21, 9, 21, 21, 1, 11, 7, 23, 5, 9, 3, 1, 23, 23, 7, 5, 3, 1, 25, 7, 11, 25, 25, 5, 13, 9, 1, 7, 11, 5, 3, 9, 1, 27, 29, 7, 11, 29, 3, 1, 29, 29, 7, 29, 5
Offset: 1

Views

Author

Lekraj Beedassy, May 04 2004

Keywords

Comments

Here (x,y) is considered smaller than (u,v) iff x+y < u+v or (x+y = u+v and x < u).

Examples

			A058529(6) = 41; (3, 5), (7, 2), (11, 9), (13, 8), ... are pairs satisfying x^2 - 2*y^2 = -+41; (3, 5) is the smallest one, so a(6) = 3.

Crossrefs

Cf. A058529, A094137, A094138.

Programs

  • PARI
    {sp(d)=local(m,b,z,x,y);m=d+2;b=1;z=1;while(b&&z1&&v[k]<7,b=0));if(b>0,print1(sp(n)[1],",")))}

Extensions

Edited, corrected and extended by Klaus Brockhaus May 31 2004

A094138 Values x+y of smallest pair (x,y) satisfying x^2 - 2*y^2=-+d, where d=A058529(n).

Original entry on oeis.org

2, 3, 4, 6, 5, 8, 8, 6, 7, 11, 10, 10, 8, 13, 13, 11, 9, 14, 16, 10, 14, 13, 18, 11, 16, 16, 14, 19, 12, 21, 17, 20, 19, 13, 20, 23, 18, 16, 14, 21, 21, 20, 19, 17, 15, 22, 25, 25, 23, 22, 16, 28, 23, 28, 21, 26, 19, 17, 25, 24, 24, 22, 20, 18, 29, 25, 30, 28, 27, 23, 33, 28, 19
Offset: 1

Views

Author

Lekraj Beedassy, May 04 2004

Keywords

Comments

Here (x,y) is considered smaller than (u,v) iff x+y < u+v or (x+y = u+v and x < u).

Examples

			A058529(14) = 103; (5, 8), (11, 3), (17, 14), (21, 13), ... are pairs satisfying x^2 - 2*y^2 = -+103; (5, 8) is the smallest one, so a(14) = 5+8 = 13.

Crossrefs

Cf. A058529, A094136, A094137.

Programs

  • PARI
    {for(n=1,690,fac=factor(n);v=vector(matsize(fac)[1],j,fac[j,1])%8;b=1;for(k=1,length(v),if(v[k]>1&&v[k]<7,b=0));if(b>0,print1(sp(n)[3],",")))} \\ For sp(n) see A094136.

Extensions

Edited, corrected and extended by Klaus Brockhaus May 31 2004

A094140 Smallest inradius of primitive Pythagorean triangle whose legs differ by A058529(n).

Original entry on oeis.org

1, 2, 3, 5, 4, 14, 7, 5, 6, 18, 9, 21, 7, 33, 22, 11, 8, 45, 39, 9, 13, 30, 60, 10, 30, 15, 33, 84, 11, 68, 60, 51, 34, 12, 91, 95, 65, 39, 13, 57, 38, 19, 70, 42, 14, 105, 84, 144, 42, 21, 15, 138, 112, 115, 80, 92, 48, 16, 46, 23, 119, 85, 51, 17, 100, 126, 209, 75, 50, 25
Offset: 1

Views

Author

Lekraj Beedassy, May 04 2004

Keywords

Comments

This is the product x*y of the smallest positive solution (x,y) to x^2 - 2*y^2 = -+d, where d=A058529(n).

References

  • Mohammad K. Azarian, Circumradius and Inradius, Problem S125, Math Horizons, Vol. 15, Issue 4, April 2008, p. 32. Solution published in Vol. 16, Issue 2, November 2008, p. 32.

Crossrefs

Cf. A058529, A094136, A094137, A094138, A094142, A094143.

Extensions

Corrected and extended by Ray Chandler, Jun 20 2004

A094142 Smallest semiperimeter of primitive Pythagorean triangle whose legs differ by A058529(n).

Original entry on oeis.org

6, 15, 28, 42, 45, 99, 72, 66, 91, 143, 110, 170, 120, 238, 195, 156, 153, 322, 304, 190, 210, 299, 437, 231, 323, 272, 350, 589, 276, 525, 493, 460, 399, 325, 660, 696, 558, 464, 378, 550, 483, 420, 627, 527, 435, 814, 725, 1025, 575, 506, 496, 1015, 897, 924
Offset: 1

Views

Author

Lekraj Beedassy, May 04 2004

Keywords

Comments

This is the product m*(m+y), with m=x+y, of the smallest positive solution pair (x, y) to x^2 - 2*y^2 = -+d, where d=A058529(n).

Crossrefs

Cf. A058529, A094136, A094137, A094138, A094140, A094143.

Extensions

Corrected and extended by Ray Chandler, Jun 20 2004

A094143 Least area of primitive Pythagorean triangle whose legs differ by A058529(n).

Original entry on oeis.org

6, 30, 84, 210, 180, 1386, 504, 330, 546, 2574, 990, 3570, 840, 7854, 4290, 1716, 1224, 14490, 11856, 1710, 2730, 8970, 26220, 2310, 9690, 4080, 11550, 49476, 3036, 35700, 29580, 23460, 13566, 3900, 60060, 66120, 36270, 18096, 4914, 31350, 18354, 7980
Offset: 1

Views

Author

Lekraj Beedassy, May 04 2004

Keywords

Examples

			This is product of A094140(n) and A094142(n).

Crossrefs

Cf. A058529, A094136, A094137, A094138, A094140, A094142.

Extensions

Corrected and extended by Ray Chandler, Jun 20 2004
Showing 1-5 of 5 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.