OFFSET
1,1
COMMENTS
Inspired by Project Euler, Problem 143 (see link).
For the corresponding primitive triples and miscellaneous properties and references, see A336328.
If FA + FB + FC = d, then we have this "beautifully symmetric equation" between a, b, c and d (see Martin Gardner):
3*(a^4 + b^4 + c^4 + d^4) = (a^2 + b^2 + c^2 + d^2)^2.
This sequence is not increasing. For example, a(2) = 73 for triangle with largest side = 95 while a(3) = 43 for triangle with largest side = 152.
REFERENCES
Martin Gardner, Mathematical Circus, Elegant triangles, First Vintage Books Edition, 1979, p. 65.
LINKS
FORMULA
a(n) = A336328(n, 1).
EXAMPLE
a(1) = 57 because the first triple is (57, 65, 73) with corresponding d = FA + FB + FC = 264/7 + 195/7 + 325/7 = 112 and the symmetric relation satisfies: 3*(57^4 + 65^4 + 73^4 + 112^4) = (57^2 + 65^2 + 73^2 + 112^2)^2 = 642470409.
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Jul 21 2020
STATUS
approved