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

1,2

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

Cf. A266212.

Sequence in context: A352754 A090785 A069482 * A102045 A055508 A274356

Adjacent sequences: A274009 A274010 A274011 * A274013 A274014 A274015

Keyword

nonn

Author

Altug Alkan, Jun 06 2016

Status

approved