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.

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A227206 Largest number in an integer 6-tuple (a, b, c, d, e, f) satisfying the Markoff(6) equation a^2+b^2+c^2+d^2+e^2+f^2 = 6*a*b*c*d*e*f.

Original entry on oeis.org

1, 5, 29, 169, 869, 985, 5741, 26041, 29405, 33461, 151201, 195025, 756029, 780361, 998789, 1136689, 5116301, 6625109, 23384789, 26308105, 29816641, 33929309, 38613965, 135777769, 225058681, 657744361, 678888869, 700763309, 788361985, 864683429, 890206969, 1012771061, 1152597605
Offset: 1

Views

Author

Shanzhen Gao, Sep 18 2013

Keywords

Comments

2*a(n)^2-1 is a square for a(1), a(2), a(3), a(4), a(6), a(7), a(10), a(12), a(16), a(18), a(23), a(25),...

Examples

			1 is in the sequence since (1, 1, 1, 1, 1, 1) is a solution to a^2+b^2+c^2+d^2+e^2+f^2 = 6*a*b*c*d*e*f. 5, 29, and 169 are in the sequence since (5, 1, 1, 1, 1, 1), (29, 5, 1, 1, 1, 1), (169, 29, 1, 1, 1, 1) are solutions.

Crossrefs

Cf. A001653, A229242 (Markoff(5)).

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.

Original entry on oeis.org

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

Views

Author

Giorgos Kalogeropoulos, Oct 18 2020

Keywords

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.

Examples

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

Crossrefs

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

Programs

  • 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
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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