A038862 Numbers ending with '7' that are the difference of two positive cubes.

7, 37, 117, 127, 217, 387, 397, 547, 657, 817, 1027, 1197, 1267, 1387, 1647, 1657, 1727, 2107, 2437, 2457, 2717, 2977, 3087, 3367, 3997, 4167, 4447, 4697, 4977, 5167, 5677, 5707, 6327, 6347, 6487, 6517, 7057, 7317, 7657, 7957, 8587, 8937, 9197, 9317

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A181123.

Programs

Maple

filter:= proc(n) local t,y,r;
  for t in sort(convert(numtheory:-divisors(n),list))  do
    r:= 12*n*t-3*t^4;
    if r < 0 then return false fi;
    if not issqr(r) then next fi;
    y:= (sqrt(r)-3*t^2)/(6*t);
    if y::posint then return true fi
  od;
  false
end proc:
select(filter, [seq(i,i=7..10000,10)]); # Robert Israel, Aug 08 2019

Mathematica

With[{nn=60},Select[Union[#[[2]]-#[[1]]&/@Subsets[Range[nn]^3,{2}]],Mod[#,10] == 7&&#Harvey P. Dale, Jan 12 2022 *)

Extensions

Name corrected by Robert Israel, Aug 08 2019