OFFSET
1,1
COMMENTS
Corresponding values of n^2 + 1 are 990026, 1418482, 2585665, 4198402, 15904145, 21013057, 23213125, ...
Prime terms of this sequence are 6323, 38501, 159013, 161573, ...
Sequence focuses on the noncube values of n in order to eliminate trivial solutions of motivation equation that is n^2 + 1 = x^3 + y^3 where x and y are positive integers.
Union of this sequence and all positive cubes give the integers n such that n^2 + 1 are the sum of 2 positive cubes.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..330
EXAMPLE
995 is a term because 995^2 + 1 = 990026 = 51^3 + 95^3.
1191 is a term because 1191^2 + 1 = 1418482 = 85^3 + 93^3.
1608 is a term because 1608^2 + 1 = 2585665 = 76^3 + 129^3.
PROG
(PARI) T = thueinit('z^3+1);
is(n) = #select(v->min(v[1], v[2])>0, thue(T, n))>0;
for(n=2, 200000, if(is(n^2+1) && ispower(n, 3) == 0, print1(n, ", ")))
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 10 2016
STATUS
approved