A386285 -id:A386285 - cp's OEIS frontend

A386286 Values of v in the quartets (3, u, v, w) of type 2; i.e., values of v for solutions to 3(3 + u) = v(v - w), in positive integers, with v > 1, sorted by nondecreasing values of u; see A386285.

6, 12, 15, 21, 6, 12, 24, 27, 6, 15, 30, 33, 18, 36, 39, 7, 21, 42, 9, 45, 8, 12, 24, 48, 51, 27, 54, 57, 10, 12, 15, 30, 60, 9, 63, 11, 33, 66, 69, 9, 12, 18, 36, 72, 15, 75, 13, 39, 78, 81, 12, 14, 21, 42, 84, 87, 10, 15, 18, 45, 90, 93, 12, 16, 24, 48, 96

Offset: 1

Clark Kimberling, Aug 12 2025

nonn

Cf. A386285.

A386287 Values of w in the quartets (3, u, v, w) of type 2; i.e., values of v for solutions to 3(3 + u) = v(v - w), in distinct positive integers, with v > 1, sorted by nondecreasing values of u; see A386285.

Original entry on oeis.org

4, 11, 14, 20, 2, 10, 23, 26, 1, 13, 29, 32, 16, 35, 38, 1, 19, 41, 4, 44, 2, 8, 22, 47, 50, 25, 53, 56, 4, 7, 11, 28, 59, 2, 62, 5, 31, 65, 68, 1, 6, 14, 34, 71, 10, 74, 7, 37, 77, 80, 5, 8, 17, 40, 83, 86, 1, 9, 13, 43, 89, 92, 4, 10, 20, 46, 95, 2, 98, 11

Offset: 1

Clark Kimberling, Aug 12 2025

Cf. A386285.

A385879 Values of u in triples (u, v, w) such that the polynomial x^3 + ux^2 + vx + w has 3 (possibly repeated) negative integer zeros; the triples are ordered by the inequality u < v.

Original entry on oeis.org

3, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14

Offset: 1

Clark Kimberling, Jul 11 2025

nonn

			First 20 triples:
    u    v    w
    3    3    1
    4    5    2
    5    7    3
    5    8    4
    6    9    4
    6   11    6
    6   12    8
    7   11    5
    7   14    8
    7   15    9
    7   16   12
    8   13    6
    8   17   10
    8   19   12
    8   20   16
    8   21   18
    9   15    7
    9   20   12
    9   23   15
    9   24   16
(x + 1)^3 = x^3 + 3*x^2 + 3*x + 1, so (3, 3, 1) is in the list; here the negative zeros are -1, -1, and -1.

Cf. A385880, A386285, A386286.

z = 120;
t = Table[{b + c + d, c  d + d  b + b  c, b  c  d}, {b, 1, z}, {c, 1, z}, {d, 1, z}];
t1 = Union[Flatten[t, 2]]; t2 = Take[t1, 40]
Grid[t2]

cp's OEIS Frontend

A386286 Values of v in the quartets (3, u, v, w) of type 2; i.e., values of v for solutions to 3(3 + u) = v(v - w), in positive integers, with v > 1, sorted by nondecreasing values of u; see A386285.

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A386287 Values of w in the quartets (3, u, v, w) of type 2; i.e., values of v for solutions to 3(3 + u) = v(v - w), in distinct positive integers, with v > 1, sorted by nondecreasing values of u; see A386285.

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A385879 Values of u in triples (u, v, w) such that the polynomial x^3 + ux^2 + vx + w has 3 (possibly repeated) negative integer zeros; the triples are ordered by the inequality u < v.

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cp's OEIS Frontend

A386286 Values of v in the quartets (3, u, v, w) of type 2; i.e., values of v for solutions to 3(3 + u) = v(v - w), in positive integers, with v > 1, sorted by nondecreasing values of u; see A386285.

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Author

Keywords

Crossrefs

A386287 Values of w in the quartets (3, u, v, w) of type 2; i.e., values of v for solutions to 3(3 + u) = v(v - w), in distinct positive integers, with v > 1, sorted by nondecreasing values of u; see A386285.

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Author

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Crossrefs

A385879 Values of u in triples (u, v, w) such that the polynomial x^3 + u*x^2 + v*x + w has 3 (possibly repeated) negative integer zeros; the triples are ordered by the inequality u < v.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

A385879 Values of u in triples (u, v, w) such that the polynomial x^3 + ux^2 + vx + w has 3 (possibly repeated) negative integer zeros; the triples are ordered by the inequality u < v.