[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A355490
Numbers of the form a+b+c = a^2 - b^2 - c^2 where a > b >= c > 0.
2
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
KEYWORD
nonn
AUTHOR
Mohammad Arab, Jul 04 2022
EXTENSIONS
a(57) = 184 inserted by Charles R Greathouse IV, Jul 05 2022
STATUS
approved