A386288 -id:A386288 - cp's OEIS frontend

A386697 Values of v in the quartets (4, u, v, w) of type 2; i.e., values of v for solutions to 4(4 + u) = v(v - w), in distinct positive integers, with v > 1, sorted by nondecreasing values of u; see A386288.

10, 20, 8, 12, 24, 14, 28, 12, 18, 36, 8, 20, 40, 22, 44, 16, 24, 48, 26, 52, 8, 28, 56, 12, 20, 30, 60, 32, 64, 34, 68, 9, 12, 24, 36, 72, 38, 76, 10, 40, 80, 12, 14, 28, 42, 84, 11, 44, 88, 46, 92, 16, 32, 48, 96, 20, 50, 100, 13, 52, 104, 12, 18, 36, 54

Offset: 1

Clark Kimberling, Aug 16 2025

nonn

Cf. A386288.

A386698 Values of w in the quartets (4, u, v, w) of type 2; i.e., values of w for solutions to 4(4 + u) = v(v - w), in distinct positive integers, with v > 1, sorted by nondecreasing values of u; see A386288.

Original entry on oeis.org

8, 19, 5, 10, 23, 12, 27, 9, 16, 35, 3, 18, 39, 20, 43, 13, 22, 47, 24, 51, 1, 26, 55, 7, 17, 28, 59, 30, 63, 32, 67, 1, 6, 21, 34, 71, 36, 75, 2, 38, 79, 5, 8, 25, 40, 83, 3, 42, 87, 44, 91, 10, 29, 46, 95, 15, 48, 99, 5, 50, 103, 3, 12, 33, 52, 107, 6, 9

Offset: 1

Clark Kimberling, Aug 16 2025

Cf. A386288.

A385880 Values of u in triples (u, v, w) such that the polynomial x^3 + ux^2 + vx + w has 3 distinct negative integer zeros; the triples are ordered by the inequality u < v.

Original entry on oeis.org

6, 7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16

Offset: 1

Clark Kimberling, Jul 11 2025

nonn

			First 20 triples:
  u    v    w
  6   11    6
  7   14    8
  8   17   10
  8   19   12
  9   20   12
  9   23   15
  9   26   24
 10   23   14
 10   27   18
 10   29   20
 10   31   30
 11   26   16
 11   31   21
 11   34   24
 11   36   36
 11   38   40
 12   29   18
 12   35   24
 12   39   28
 12   41   30

Cf. A385779, A386287, A386288.

z = 140;
t = Table[{b + c + d, c  d + d  b + b  c, b  c  d}, {b, 1, z - 2}, {c, b + 1, z - 1}, {d, c + 1, z}];
t1 = Union[Flatten[t, 2]];
t2 = Take[t1, 20]
Grid[t2]

cp's OEIS Frontend

A386697 Values of v in the quartets (4, u, v, w) of type 2; i.e., values of v for solutions to 4(4 + u) = v(v - w), in distinct positive integers, with v > 1, sorted by nondecreasing values of u; see A386288.

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A386698 Values of w in the quartets (4, u, v, w) of type 2; i.e., values of w for solutions to 4(4 + u) = v(v - w), in distinct positive integers, with v > 1, sorted by nondecreasing values of u; see A386288.

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A385880 Values of u in triples (u, v, w) such that the polynomial x^3 + ux^2 + vx + w has 3 distinct negative integer zeros; the triples are ordered by the inequality u < v.

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cp's OEIS Frontend

A386697 Values of v in the quartets (4, u, v, w) of type 2; i.e., values of v for solutions to 4(4 + u) = v(v - w), in distinct positive integers, with v > 1, sorted by nondecreasing values of u; see A386288.

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A386698 Values of w in the quartets (4, u, v, w) of type 2; i.e., values of w for solutions to 4(4 + u) = v(v - w), in distinct positive integers, with v > 1, sorted by nondecreasing values of u; see A386288.

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A385880 Values of u in triples (u, v, w) such that the polynomial x^3 + u*x^2 + v*x + w has 3 distinct negative integer zeros; the triples are ordered by the inequality u < v.

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Mathematica

A385880 Values of u in triples (u, v, w) such that the polynomial x^3 + ux^2 + vx + w has 3 distinct negative integer zeros; the triples are ordered by the inequality u < v.