A363835 Numbers that are the concatenation of a square and a cube, and also the concatenation of a cube and a square.

10, 11, 164, 640, 641, 1441, 1729, 1961, 6464, 7290, 7291, 14096, 40960, 40961, 64729, 72964, 115625, 116641, 125441, 146656, 148841, 156250, 156251, 409664, 466560, 466561, 644096, 729729, 1117649, 1166464, 1176490, 1176491, 1262144, 1531441, 1562564, 1795664, 2621440, 2621441, 4096729, 4665664

Offset

1,1

Comments

Includes 10*x^6 and 10*x^6 + 1 for all x >= 1.

Links

Robert Israel, Table of n, a(n) for n = 1..1738

Example

a(6) = 1441 is the concatenation of 1^3 and 21^2 and also the concatenation of 12^2 and 1^3.

Maple

N:= 7: # for terms of up to N digits
for d from 1 to N-1 do
  S[d]:= {seq(i^2, i=ceil(10^((d-1)/2)) .. floor((10^d-1)^(1/2)))}:
  C[d]:= {seq(i^3, i=ceil(10^((d-1)/3)) .. floor((10^d-1)^(1/3)))}:
od:
SC:= {seq(seq(seq(seq(10^i*s+c, s=S[j]), c=C[i]), j=1..N-i), i=1..N-1), seq(seq(10*s, s=S[i]), i=1..N-1)}:
CS:= {seq(seq(seq(seq(10^i*c+s, c=C[j]), s=S[i]), j=1..N-i), i=1..N-1), seq(seq(10*c, c=C[i]), i=1..N-1)}:
sort(convert(SC intersect CS, list));

Crossrefs

Cf. A000290, A000578.

Sequence in context: A222473 A361990 A335801 * A041217 A041218 A300458

Adjacent sequences: A363832 A363833 A363834 * A363836 A363837 A363838

Keyword

nonn,base

Author

Robert Israel, Oct 19 2023

Status

approved