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A274012
Integers n such that n^3 is the average of a nonzero square and a nonzero fourth power.
1
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)
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
KEYWORD
nonn
AUTHOR
Altug Alkan, Jun 06 2016
STATUS
approved