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 1-10 of 14 results. Next

A088557 Least even leg of primitive Pythagorean triangles with odd leg 2n+1.

Original entry on oeis.org

4, 12, 24, 40, 60, 84, 8, 144, 180, 20, 264, 312, 364, 420, 480, 56, 12, 684, 80, 840, 924, 28, 1104, 1200, 140, 1404, 48, 176, 1740, 1860, 16, 72, 2244, 260, 2520, 2664, 308, 36, 3120, 3280, 3444, 132, 416, 3960, 60, 476, 168, 4704, 20, 5100, 5304, 88, 5724, 5940
Offset: 1

Views

Author

Lekraj Beedassy, Nov 17 2003

Keywords

Comments

a(n) shares identical entries with A046092(n) except for n=(A081934 - 1)/2.

Links

Crossrefs

Cf. A088558, A096891-A096900.

Programs

  • Mathematica
    a[n_] := 2k /. Solve[k > 0 && 1 < h < 2k + 2n + 1 && (2k)^2 + (2n + 1)^2 == h^2 && GCD[2k, 2n + 1, h] == 1, {k, h}, Integers][[1]];
a /@ Range[54] (* Jean-François Alcover, Mar 05 2020 *)

Extensions

Corrected and extended by Ray Chandler, Jul 14 2004

A088558 Least odd leg of primitive Pythagorean triangles with even leg 4n.

Original entry on oeis.org

3, 15, 5, 63, 21, 7, 45, 255, 77, 9, 117, 55, 165, 33, 11, 1023, 285, 65, 357, 39, 13, 105, 525, 247, 621, 153, 725, 15, 837, 119, 957, 4095, 85, 273, 51, 17, 1365, 345, 133, 231, 1677, 95, 1845, 57, 19, 513, 2205, 1015, 2397, 609, 253, 105, 2805, 713, 21, 207, 325
Offset: 1

Views

Author

Lekraj Beedassy, Nov 17 2003

Keywords

Links

Crossrefs

Cf. A088557, A096891-A096900.

Programs

  • Mathematica
    a[n_] := 2k + 1 /. Solve[k > 0 && 1 < h < 2k + 1 + 4n && (2k + 1)^2 + (4n)^2 == h^2 && GCD[2k + 1, 4n, h] == 1, {k, h}, Integers][[1]];
a /@ Range[57] (* Jean-François Alcover, Mar 05 2020 *)

Extensions

Extended by Ray Chandler, Jul 14 2004

A096900 a(n) = (A088558(n)-1)/2.

Original entry on oeis.org

1, 7, 2, 31, 10, 3, 22, 127, 38, 4, 58, 27, 82, 16, 5, 511, 142, 32, 178, 19, 6, 52, 262, 123, 310, 76, 362, 7, 418, 59, 478, 2047, 42, 136, 25, 8, 682, 172, 66, 115, 838, 47, 922, 28, 9, 256, 1102, 507, 1198, 304, 126, 52, 1402, 356, 10, 103, 162, 412, 1738, 80, 1858
Offset: 1

Views

Author

Ray Chandler, Jul 14 2004

Keywords

Crossrefs

Cf. A088557, A088558, A096891-A096900.

A155185 Primes in A155175.

Original entry on oeis.org

5, 13, 113, 1741, 5101, 8581, 9941, 21841, 26681, 47741, 82013, 481181, 501001, 1009621, 2356621, 2542513, 3279361, 3723721, 4277813, 7757861, 8124481, 13204661, 25311613, 30772013, 44170601, 48619661, 51521401, 52541501, 54236113, 60731221, 72902813
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

Keywords

Comments

Hypotenuse C (prime numbers only) of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, ar=a*b/2; s=a+b+c, s-+1 are primes. p=1,q=2,a=3,b=4,c=5=prime,s=12-+1primes, ...

Crossrefs

Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, A096891, A066885, A099776, A110494, A081589

Programs

  • Mathematica
    lst={};Do[p=n;q=p+1;a=q^2-p^2;c=q^2+p^2;b=2*p*q;ar=a*b/2;s=a+b+c;If[PrimeQ[s-1]&&PrimeQ[s+1],If[PrimeQ[c],AppendTo[lst,c]]],{n,8!}];lst (* corrected by Ray Chandler, Feb 11 2020 *)

Extensions

Sequence corrected by Ray Chandler, Feb 11 2020

A096892 Least semiperimeter of primitive Pythagorean triangles with odd leg 2n+1.

Original entry on oeis.org

6, 15, 28, 45, 66, 91, 20, 153, 190, 35, 276, 325, 378, 435, 496, 77, 42, 703, 104, 861, 946, 63, 1128, 1225, 170, 1431, 88, 209, 1770, 1891, 72, 117, 2278, 299, 2556, 2701, 350, 99, 3160, 3321, 3486, 187, 464, 4005, 130, 527, 228, 4753, 110, 5151, 5356, 165
Offset: 1

Views

Author

Ray Chandler, Jul 14 2004

Keywords

Crossrefs

Cf. A088557, A088558, A096891-A096900.

A096893 Least area/6 of primitive Pythagorean triangles with odd leg 2n+1.

Original entry on oeis.org

1, 5, 14, 30, 55, 91, 10, 204, 285, 35, 506, 650, 819, 1015, 1240, 154, 35, 2109, 260, 2870, 3311, 105, 4324, 4900, 595, 6201, 220, 836, 8555, 9455, 84, 390, 12529, 1495, 14910, 16206, 1925, 231, 20540, 22140, 23821, 935, 3016, 29370, 455, 3689, 1330
Offset: 1

Views

Author

Ray Chandler, Jul 14 2004

Keywords

Crossrefs

Cf. A088557, A088558, A096891-A096900.

A096894 Least inradius of primitive Pythagorean triangles with odd leg 2n+1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 3, 8, 9, 6, 11, 12, 13, 14, 15, 12, 5, 18, 15, 20, 21, 10, 23, 24, 21, 26, 15, 24, 29, 30, 7, 20, 33, 30, 35, 36, 33, 14, 39, 40, 41, 30, 39, 44, 21, 42, 35, 48, 9, 50, 51, 28, 53, 54, 51, 56, 45, 18, 35, 60, 57, 62, 63, 60, 65, 42, 55, 68, 69, 66, 11, 60, 69, 74
Offset: 1

Views

Author

Ray Chandler, Jul 14 2004

Keywords

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. A088557, A088558, A096891-A096900.

A096895 a(n) = A088557(n)/4.

Original entry on oeis.org

1, 3, 6, 10, 15, 21, 2, 36, 45, 5, 66, 78, 91, 105, 120, 14, 3, 171, 20, 210, 231, 7, 276, 300, 35, 351, 12, 44, 435, 465, 4, 18, 561, 65, 630, 666, 77, 9, 780, 820, 861, 33, 104, 990, 15, 119, 42, 1176, 5, 1275, 1326, 22, 1431, 1485, 170, 1596, 63, 11, 30, 1830
Offset: 1

Views

Author

Ray Chandler, Jul 14 2004

Keywords

Crossrefs

Cf. A088557, A088558, A096891-A096900.

A096896 Least hypotenuse of primitive Pythagorean triangles with even leg 4n.

Original entry on oeis.org

5, 17, 13, 65, 29, 25, 53, 257, 85, 41, 125, 73, 173, 65, 61, 1025, 293, 97, 365, 89, 85, 137, 533, 265, 629, 185, 733, 113, 845, 169, 965, 4097, 157, 305, 149, 145, 1373, 377, 205, 281, 1685, 193, 1853, 185, 181, 545, 2213, 1033, 2405, 641, 325, 233, 2813, 745
Offset: 1

Views

Author

Ray Chandler, Jul 14 2004

Keywords

Crossrefs

Cf. A088557, A088558, A096891-A096900.

A096897 Least semiperimeter of primitive Pythagorean triangles with even leg 4n.

Original entry on oeis.org

6, 20, 15, 72, 35, 28, 63, 272, 99, 45, 143, 88, 195, 77, 66, 1056, 323, 117, 399, 104, 91, 165, 575, 304, 675, 221, 783, 120, 899, 204, 1023, 4160, 187, 357, 170, 153, 1443, 437, 247, 336, 1763, 228, 1935, 209, 190, 621, 2303, 1120, 2499, 725, 391, 273, 2915
Offset: 1

Views

Author

Ray Chandler, Jul 14 2004

Keywords

Crossrefs

Cf. A088557, A088558, A096891-A096900.
Showing 1-10 of 14 results. Next

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