A383102 Cubes that are concatenations of two or more positive cubes.

27818127, 27818127000, 216648648216, 27818127000000, 125112533753375, 216648648216000, 27000810008100027, 27818127000000000, 125112533753375000, 216648648216000000, 27000810008100027000, 27818127000000000000, 125112533753375000000, 216000648000648000216, 216648648216000000000

Offset

1,1

Comments

If k is a term, then so is 1000*k.

Contains 27 * (10^(3*k+2)+1)^3 for k >= 0.

Links

Table of n, a(n) for n=1..15.

Example

a(3) = 216648648216 = 6006^3 is a term because it is the concatenation of 6^3 = 216, 4^3 = 64, 2^3 = 8, 4^3 = 64, 2^3 = 9 and 6^3 = 216.

Maple

g:= proc(x) local j, y;
      for j from 1 to ilog10(x) do
        y:= x mod 10^j;
        if y < 10^(j-1) then next fi;
        if surd(y, 3)::integer and h((x-y)/10^j) then return true fi;
       od;
       false
end proc:
h:= proc(x) option remember; local j, y;
      if surd(x, 3)::integer then return true fi;
      for j from 1 to ilog10(x) do
        y:= x mod 10^j;
        if y < 10^(j-1) then next fi;
        if surd(y, 3)::integer and procname((x-y)/10^j) then return true fi;
       od;
       false
end proc:
select(g, [seq(x^3, x = 1 .. 10^7)]);

Crossrefs

Subsequence of A019548. Cf. A009421.

Sequence in context: A018187 A275612 A275613 * A204805 A216903 A114681

Adjacent sequences: A383099 A383100 A383101 * A383103 A383104 A383105

Keyword

nonn,base

Author

Robert Israel, Apr 16 2025

Status

approved