OFFSET
1,2
COMMENTS
Numbers n such that 2*n^3 = x^2 + y^4 where x and y are nonzero integers, is soluble.
Square terms of this sequence are 1, 16, 25, 81, 256, 400, 625, 841, 1225, 1296, 1681, 2025, 2401, ...
From David A. Corneth, Jun 06 2016 (Start):
A000351, the powers of 5, is a subsequence.
If n is a term, then n * k^4 is a term; as 2*n^3 = x^4 + y^2, 2 * (n * k^4)^3 = (k^3 * x)^4 + (k^6 * y)^2. (End)
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000
EXAMPLE
5 is a term because 5^3 = (13^2 + 3^4) / 2.
PROG
(PARI) is(n) = for(x=1, (2*n) ^ 0.75, if(issquare(2*n^3 - x^4)&&2*n^3-x^4>0, return(1)); 0) \\ David A. Corneth, Jun 06 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Jun 06 2016
STATUS
approved