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 A080761 Positive numbers of the form y^2 - x^3, x and y >= 1. 4
 1, 3, 8, 9, 12, 15, 17, 18, 19, 22, 24, 28, 30, 35, 36, 37, 38, 40, 41, 44, 48, 54, 55, 56, 57, 63, 64, 65, 68, 71, 73, 79, 80, 89, 92, 94, 97, 98, 99, 100, 101, 105, 106, 107, 108, 112, 113, 117, 119, 120, 121, 128, 129, 131, 132, 136, 138, 141, 142, 143, 145, 148, 151 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Comments from Artur Jasinski, Oct 03 2007 (Start): Some numbers have multiple partitions:   8 = 4^2 - 8^3 = 312^2 - 46^3   9 = 6^2 - 3^3 = 15^2 - 6 ^3 = 253^2 - 40^3 (End) This is Mordell's equation with the condition that x and y are positive. Sequence A054504 lists the n for which there is no solution to Mordell's equation. Hence, none of those numbers will be in this sequence. The terms of this sequence can be determined by looking at the link to Gebel's data. - T. D. Noe, Mar 23 2011 REFERENCES J. Gebel, A. Petho and H. G. Zimmer, On Mordell's equation, Compositio Mathematica 110 (3) (1998), 335-367. LINKS J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017] Cino Hilliard, Proof that n^3+7 <> k^2 for all integers n,k. EXAMPLE 8 is in the sequence since 3^2 = 1^3 + 8. MATHEMATICA With[{nn=100}, Take[Union[Select[First[#]^2-Last[#]^3&/@Tuples[Range[ 20nn], 2], #>0&]], nn]] (* Harvey P. Dale, Jul 10 2012 *) PROG (PARI) diop(n, m) = { for(p=1, m, for(x=1, n, y=x*x*x+p; if(issquare(y), print1(p" "); break) ) ) } CROSSREFS Complement of A080762. Cf. sequences for n^3+7, n^3+17, n^3+3, n^3+2, n^3+5. Cf. A029727, A029728, A134042, A134043. Sequence in context: A028960 A139491 A084387 * A087286 A165289 A066494 Adjacent sequences:  A080758 A080759 A080760 * A080762 A080763 A080764 KEYWORD nonn AUTHOR Cino Hilliard, Mar 10 2003 EXTENSIONS "Positive" added to definition by N. J. A. Sloane, Oct 06 2007 STATUS approved

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Last modified October 24 05:38 EDT 2021. Contains 348217 sequences. (Running on oeis4.)