A274012 Integers n such that n^3 is the average of a nonzero square and a nonzero fourth power.

1, 5, 16, 25, 26, 40, 41, 50, 80, 81, 125, 250, 256, 365, 386, 400, 405, 416, 425, 450, 457, 477, 625, 626, 640, 656, 800, 841, 845, 1000, 1125, 1153, 1210, 1225, 1280, 1296, 1681, 1825, 2000, 2025, 2057, 2106, 2197, 2312, 2401, 3042, 3125, 3240, 3250, 3321, 3362, 3400, 3625

Offset: 1

Author

Altug Alkan, Jun 06 2016

Keywords

• nonn

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)

Examples

			5 is a term because 5^3 = (13^2 + 3^4) / 2.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A266212.

Programs

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