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

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

1,1

Comments

It seems that A082867 is a subsequence.

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

Links

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

Example

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.

Mathematica

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]

Prog

(PARI) 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

Crossrefs

Cf. A082867, A082772, A134582, A355491.

Sequence in context: A014544 A237610 A122754 * A082867 A075713 A374476

Adjacent sequences: A355487 A355488 A355489 * A355491 A355492 A355493

Keyword

nonn

Author

Mohammad Arab, Jul 04 2022

Extensions

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

Status

approved