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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 (list; graph; refs; listen; history; text; internal format)
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
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

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Last modified September 12 05:07 EDT 2024. Contains 375842 sequences. (Running on oeis4.)