A338256 Generalized Markoff numbers: union of numbers a, b, c, d, e satisfying the Markoff(5) equation a^2 + b^2 + c^2 + d^2 + e^2 = a*b*c*d*e.

1, 3, 4, 5, 9, 12, 23, 31, 33, 35, 44, 57, 60, 81, 107, 123, 157, 179, 204, 212, 273, 293, 311, 369, 391, 411, 417, 459, 555, 620, 657, 679, 1076, 1115, 1187, 1259, 1275, 1308, 1377, 1453, 1713, 1813, 1979, 2508, 2604, 2673, 2764, 2817, 2885, 3419, 3475, 3804, 3849

Offset

1,2

Comments

Every term of A229240 is a term of this sequence.

Also, union of positive integers satisfying Hurwitz equation (x_1)^2 + (x_2)^2 + ... + (x_n)^2 = z * x_1 * x_2 * ... * x_n for z=1 and n=5.

Links

Table of n, a(n) for n=1..53.

Example

{1259,35,4,3,3} is a solution and that is why 3,4,35,1259 belong to the sequence.

Mathematica

div={1, 3}; limit=10^4; Monitor[Do[m=div[[{a, b, c, d}]]; m1=Times@@m; m2=Tr[m^2]; s=Sqrt[m1^2-4m2]; x1=(m1-s)/2; x2=(m1+s)/2; If[IntegerQ[x1]&&x2<limit, AppendTo[div, {x1, x2}]]; div=Union@Flatten@div, {n, 5}, {a, l=Length@div}, {b, a}, {c, b}, {d, c}], {"stops when", l-a, "is equal to 0"}]; div

Crossrefs

Cf. A229240, A229242, A229241, A227206, A002559.

Sequence in context: A166976 A240056 A235396 * A237132 A080633 A360374

Adjacent sequences: A338253 A338254 A338255 * A338257 A338258 A338259

Keyword

nonn

Author

Giorgos Kalogeropoulos, Oct 18 2020

Status

approved