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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 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

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