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 A070756 Numbers n such that the Diophantine equation x^4+y^5=n^4 has solutions. 1
 30, 85, 195, 240, 525, 700, 960, 1020, 1170, 1845, 2720, 3045, 3120, 4026, 4818, 5005, 5655, 6240, 7290, 7680, 7735, 7770, 9717, 11349, 11570, 12432, 13560, 15015, 16240, 16695, 16800, 17476, 20655, 22185, 22400, 22605, 23730, 27768, 30720, 32120, 32640, 32760, 34390, 37440, 40885, 42105, 43095 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Robert Israel, Oct 29 2019: (Start) The first number that occurs in more than one way is 1845, as 205^4 + 410^5 = 1476^4 + 369^5 = 1845^4. If n is a term then so is x^5*n for any x. Includes s*(s^4-t^4)/u^5 if s>t>0 and s^4 == t^4 (mod u^5), as x=t*(s^4-t^4)/u^5, y=(s^4-t^4)/u^4, n=s*(s^4-t^4)/u^5 is a solution. (End) LINKS Robert Israel, Table of n, a(n) for n = 1..100 MAPLE filter:= proc(n) local n4, y, s; n4:= n^4; for y from ceil((n4-(n-1)^4)^(1/5)) do s:= n4-y^5; if s <= 0 then return false fi; if issqr(s) and issqr(sqrt(s)) then return true fi od end proc: select(filter, [\$1..10000]); # Robert Israel, Oct 29 2019 MATHEMATICA filterQ[n_] := Module[{n4 = n^4, y, s}, For[y = Ceiling[(n4 - (n-1)^4 )^(1/5)], True, y++, s = n4 - y^5; If[s <= 0, Return[False]]; If[ IntegerQ[Sqrt[s]] && IntegerQ[Sqrt[Sqrt[s]]], Return[True]]]]; Reap[Do[If[filterQ[n], Print[n]; Sow[n]], {n, 10000}]][[2, 1]] (* Jean-François Alcover, Aug 16 2020, after Maple *) PROG (PARI) for(n=0, 500, if(sum(i=1, n, sum(j=1, i, if(i^4+j^5-n^4, 0, 1)))>0, print1(n, ", "))) CROSSREFS Sequence in context: A326838 A098996 A130862 * A058903 A254474 A103906 Adjacent sequences: A070753 A070754 A070755 * A070757 A070758 A070759 KEYWORD nonn AUTHOR Benoit Cloitre, May 14 2002 EXTENSIONS More terms from John W. Layman, Nov 25 2002 More terms from Robert Israel, Oct 29 2019 STATUS approved

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Last modified February 26 19:43 EST 2024. Contains 370352 sequences. (Running on oeis4.)