OFFSET
1,1
COMMENTS
Motivated by the search of solutions to a^n + b^(2n+2)/4 = (perfect square), which arises when searching solutions to x^n + y^(n+1) = z^(n+2) of the form x = a*z, y = b*z. It turns out that many solutions are of the form a^n = d (b^(n+1) + d), where d is a perfect power.
LINKS
Robert Israel, Table of n, a(n) for n = 1..1301
EXAMPLE
3^4 = 2^5 + 7^2; 5^4 = 7^2 + 24^2, ...
MAPLE
N:= 200: # to get terms <= N
N4:= N^4:
P:= {seq(seq(x^k, k=3..floor(log[x](N4))), x=2..floor(N4^(1/3)))}:
filter:= proc(n) local n4, Pp;
n4:= n^4;
if remove(t -> subs(t, x)<=1 or subs(t, y)<=1 or subs(t, x-y)=0, [isolve(x^2+y^2=n4)]) <> [] then return true fi;
Pp:= map(t ->n4-t, P minus {n4, n4/2});
(Pp intersect P <> {}) or (select(issqr, Pp) <> {})
end proc:
A:= select(filter, [$2..N]); # Robert Israel, May 24 2018
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, May 22 2018
STATUS
approved