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 A198444 Values x for records of minima of positive distance d between a square of integer y and a fifth power of positive integer x such that d = y^2 - x^5 (x<>k^2 and y<>k^5). 3
 1, 2, 5, 23, 27, 73, 96, 104, 396, 404, 432, 686, 723, 735, 1130, 1159, 2019, 2031, 3861, 5310, 18219, 18231, 25592, 25608, 44367, 200141, 213842, 308228, 390615, 390635, 549976, 631544, 1579129, 1657086, 2941211, 2941239, 5523608 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Distance d is equal 0 when x = k^2 and y = k^5. For d values see A198443. For y values see A198445. Conjecture (*Artur Jasinski*): For any positive number x >= A198444(n) distance d between a square of any y and a fifth power of x such that x<>k^2 and y<>k^5) can't be less than A198443(n). LINKS J. Blass, A Note on Diophantine Equation Y^2 + k = X^5, Math. Comp. 1976, Vol. 30, No. 135, pp. 638-640. A. Bremner, On the Equation Y^2 = X^5 + k, Experimental Mathematics 2008 Vol. 17, No. 3, pp. 371-374. MATHEMATICA max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^5)^(1/2)] + 1; k = m^2 - n^5; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 100000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; vecx CROSSREFS Cf. A179406, A179407, A179408, A198443, A198445. Sequence in context: A078419 A241428 A070281 * A019368 A141171 A180535 Adjacent sequences:  A198441 A198442 A198443 * A198445 A198446 A198447 KEYWORD nonn,hard AUTHOR Artur Jasinski, Oct 25 2011 STATUS approved

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Last modified February 19 13:25 EST 2020. Contains 332044 sequences. (Running on oeis4.)