Mohammad Arab - cp's OEIS frontend

User: Mohammad Arab

Mohammad Arab has authored 2 sequences.

A355491 Numbers of the form a+b+c = a^3 - b^3 - c^3 where a > b >= c > 0.

10, 35, 54, 64, 199, 235, 279, 747, 1224, 1610, 1774, 6156, 8254, 11035, 12024, 16875, 56439, 66340, 75635, 82279, 115712, 134045, 136765, 150480, 175616, 212266, 255277, 299789, 339759, 386704, 518410, 563814, 643824, 1025776, 1429190, 1431233, 1468846, 1598374

Offset: 1

Mohammad Arab, Jul 04 2022

nonn

			10 is a term: 10 = 4+3+3 = 4^3 - 3^3 - 3^3.
35 is a term: 35 = 14+13+8 = 14^3 - 13^3 - 8^3.

Cf. A355490 (with squares instead of cubes).

Solve[a==r^3-s^3-d^3 && 1<=r<=1000 && 1<=s<=1000 && 1<=d<=1000 && 0<=a && r>s>=d && a==r+s+d, {a,r,s,d}, Integers]

More terms from Jinyuan Wang, Jul 05 2022

A355490 Numbers of the form a+b+c = a^2 - b^2 - c^2 where a > b >= c > 0.

Original entry on oeis.org

8, 15, 20, 24, 27, 32, 35, 39, 44, 48, 49, 51, 54, 55, 56, 63, 64, 65, 68, 75, 80, 84, 87, 90, 92, 95, 98, 99, 104, 111, 114, 116, 119, 120, 123, 125, 128, 132, 135, 140, 143, 144, 147, 152, 153, 155, 159, 160, 164, 168, 170, 171, 174, 175, 176, 183, 184, 185, 188, 189, 195, 200, 203, 204, 207, 208, 209, 212, 215, 216, 219, 220, 224, 230, 231

Offset: 1

Mohammad Arab, Jul 04 2022

nonn

It seems that A082867 is a subsequence.

The first counterexample to the above is A082867(60) = 258. - Charles R Greathouse IV, Jul 05 2022

			8 is a term: 8 = 4+2+2 = 4^2 - 2^2 - 2^2.
15 is a term: 15 = 7+5+3 = 7^2 - 5^2 - 3^2.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A082867, A082772, A134582, A355491.

Solve[a==r^2-s^2-d^2 && 1<=r<=120 && 1<=s<=120 && 1<=d<=120 && 0<=a && r>s>=d && a==r+s+d, {a,r,s,d}, Integers]

list(lim)=my(v=List([8]));lim\=1;for(a=3,lim-2,my(a2=a^2);for(b=(sqrt(2*a^2+2*a+1)-1)\2,a-2,my(t=a2-b^2-a-b,s);if(issquare(4*t+1,&s) && (c=(s-1)/2)<=b && c<=b && a+b+c<=lim, listput(v,a+b+c)))); Set(v) \\ Charles R Greathouse IV, Jul 05 2022

a(57) = 184 inserted by Charles R Greathouse IV, Jul 05 2022

cp's OEIS Frontend

User: Mohammad Arab

A355491 Numbers of the form a+b+c = a^3 - b^3 - c^3 where a > b >= c > 0.

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