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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
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
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.)