OFFSET
1,1
COMMENTS
Since the identity n^3 + (12n)^3 = (9n)^3 + (10n)^3 holds, n < a(n) <= 12n.
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..200 (terms 1..61 from Giedrius Alkauskas).
EXAMPLE
For n = 11, a(11) = 93, since, first, 11^3 + 93^3 = 30^3 + 92^3. Second, for any integral y in the range [12, 92] there does not exist c, d, 11 < c < d < y, satisfying 11^3 + y^3 = c^3 + d^3.
MAPLE
a :=proc(n::integer) local found::boolean; local N, SQ, i;
found:=false; N:=n+1; SQ:={};
while not found do SQ:=SQ union {N^3}; N:=N+1;
for i from n+1 to N-1 do if evalb(N^3+n^3-i^3 in SQ) then
found:=true; end if; end do; end do; N end proc;
MATHEMATICA
a[n_] := a[n] = Module[{found, m, SQ, i}, found = False; m = n+1; SQ = {}; While[!found, SQ = SQ ~Union~ {m^3}; m = m+1; For[i = n+1, i <= m-1, i++, If[MemberQ[SQ, m^3+n^3-i^3], found = True]]]; m];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 200}] (* Jean-François Alcover, Feb 27 2023, after Giedrius Alkauskas's Maple code *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Giedrius Alkauskas, Feb 14 2023
STATUS
approved