A198453 -id:A198453 - cp's OEIS frontend

A198464 Consider triples a<=b

4, 8, 13, 19, 9, 13, 26, 17, 34, 43, 14, 18, 53, 32, 64, 38, 76, 19, 23, 30, 89, 103, 59, 118, 24, 28, 42, 67, 134, 151, 35, 43, 169, 29, 33, 63, 94, 188, 104, 208, 47, 58, 229, 31, 34, 38, 84, 251, 56, 137, 274, 149, 298, 39, 43, 108, 323, 52, 71, 88, 349

Offset: 1

Charlie Marion, Nov 26 2011

nonn

See A198453.

			2*5 + 3*6 = 4*7
3*6 + 7*10 = 8*11
4*7 + 12*15 = 13*16
5*8 + 18*21 = 19*22
6*9 + 6*9 = 9*12
6*9 + 11*14 = 13*16

A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.

Ron Knott, Pythagorean Triples and Online Calculators.

Cf. A103606, A198453-A198463, A198465-A198469.

A198465 Consider triples a<=b

Original entry on oeis.org

3, 3, 4, 4, 6, 7, 5, 10, 11, 6, 7, 9, 6, 15, 16, 7, 10, 12, 7, 21, 22, 8, 28, 29, 9, 11, 14, 9, 36, 37, 10, 14, 17, 10, 22, 24, 10, 45, 46, 11, 27, 29, 11, 55, 56, 12, 15, 19, 12, 21, 24, 12, 66, 67, 13, 18, 22, 13, 25, 28, 13, 78, 79, 14, 45, 47, 14, 91, 92

Offset: 1

Charlie Marion, Dec 19 2011

nonn

The definition can be generalized to define Pythagorean k-triples a<=bA198453 for more about Pythagorean k-triples.

			3*2 + 3*2 = 4*3
4*3 + 6*5 = 7*6
5*4 + 10*9 = 11*10
6*5 + 7*6 = 9*8
6*5 + 15*14 = 16*15

A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.

Ron Knott, Pythagorean Triples and Online Calculators

Cf. A103606, A198453-A198469.

A198468 Consider triples a<=b

Original entry on oeis.org

4, 7, 11, 9, 16, 12, 22, 29, 14, 37, 17, 24, 46, 29, 56, 19, 24, 67, 22, 28, 79, 47, 92, 21, 24, 37, 54, 106, 27, 42, 121, 137, 29, 53, 78, 154, 32, 59, 87, 172, 41, 50, 191, 34, 45, 55, 72, 211, 37, 42, 79, 117, 232, 128, 254, 39, 94, 277, 42, 63, 102, 301

Offset: 1

Charlie Marion, Dec 19 2011

nonn

The definition can be generalized to define Pythagorean k-triples a<=bA198453 for more about Pythagorean k-triples.

			3*2 + 3*2 = 4*3
4*3 + 6*5 = 7*6
5*4 + 10*9 = 11*10
6*5 + 7*6 = 9*8
6*5 + 15*14 = 16*15

A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.

Ron Knott, Pythagorean Triples and Online Calculators

Cf. A103606, A198453-A198469.

A379609 Triples (x,y,z) such that T(x)*T(y) = T(z) with 2 <= x <= y, where T(n) is the n-th triangular number, sorted first by values of z, then by values of x.

Original entry on oeis.org

3, 3, 8, 2, 5, 9, 4, 6, 20, 2, 20, 35, 3, 14, 35, 4, 12, 39, 5, 11, 44, 7, 10, 55, 5, 19, 75, 3, 34, 84, 9, 13, 90, 6, 21, 98, 2, 76, 132, 6, 33, 153, 4, 55, 175, 14, 18, 189, 13, 20, 195, 12, 23, 207, 15, 20, 224, 14, 22, 230, 11, 28, 231, 12, 29, 260, 7, 51, 272, 10, 38, 285, 11, 36, 296, 5, 90, 350, 3, 143, 351, 10, 50, 374, 7, 75, 399, 9, 68, 459, 19, 34, 475

Offset: 1

Kelvin Voskuijl, Dec 27 2024

			Triples begin:
  3,  3,  8;
  2,  5,  9;
  4,  6, 20;
  2, 20, 35;
  3, 14, 35;
  4, 12, 39;
  5, 11, 44;
  7, 10, 55;
  ...
The triple 2,5,9 is in this sequence because the second triangular number (3) times the fifth (15) is the ninth (45).

Cf. A000217, A188630, A198453 (additive), A225390.

A198466 Consider triples a<=b

Original entry on oeis.org

3, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 28

Offset: 1

Charlie Marion, Dec 19 2011

nonn

The definition can be generalized to define Pythagorean k-triples a<=bA198453 for more about Pythagorean k-triples.

			3*2 + 3*2 = 4*3
4*3 + 6*5 = 7*6
5*4 + 10*9 = 11*10
6*5 + 7*6 = 9*8
6*5 + 15*14 = 16*15

A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.

Ron Knott, Pythagorean Triples and Online Calculators

Cf. A103606, A198453-A198469.

A198467 Consider triples a<=b

Original entry on oeis.org

3, 6, 10, 7, 15, 10, 21, 28, 11, 36, 14, 22, 45, 27, 55, 15, 21, 66, 18, 25, 78, 45, 91, 15, 19, 34, 52, 105, 22, 39, 120, 136, 23, 50, 76, 153, 26, 56, 85, 171, 36, 46, 190, 27, 40, 51, 69, 210, 30, 36, 76, 115, 231, 126, 253, 31, 91, 276, 34, 58, 99, 300

Offset: 1

Charlie Marion, Dec 19 2011

nonn

The definition can be generalized to define Pythagorean k-triples a<=bA198453 for more about Pythagorean k-triples.

			3*2 + 3*2 = 4*3
4*3 + 6*5 = 7*6
5*4 + 10*9 = 11*10
6*5 + 7*6 = 9*8
6*5 + 15*14 = 16*15

A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.

Ron Knott, Pythagorean Triples and Online Calculators

Cf. A103606, A198453-A198469.

cp's OEIS Frontend

A198464 Consider triples a<=b

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A198465 Consider triples a<=b

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A198468 Consider triples a<=b

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A379609 Triples (x,y,z) such that T(x)*T(y) = T(z) with 2 <= x <= y, where T(n) is the n-th triangular number, sorted first by values of z, then by values of x.

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A198466 Consider triples a<=b

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A198467 Consider triples a<=b

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