A030678 Smallest nontrivial extension of n-th palindrome which is a cube.

125, 27, 343, 4096, 512, 64, 729, 8000, 9261, 110592, 226981, 3375, 4410944, 551368, 6644672, 778688, 884736, 9938375, 101194696, 111284641, 12167, 13144256, 14172488, 151419437, 16194277, 17173512, 1815848, 191102976

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A002113, A030668, A030679.

Programs

Maple

N:= 3: # to get extensions of all palindromes of <= N digits
f:= proc(n) local d,x;
  for d from 1 do
    x:= ceil((n*10^d)^(1/3));
    if x^3 < (n+1)*10^d then return x^3 fi
  od
end proc:
digrev:= proc(n) local i,L;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
Res:= seq(f(i),i=1..9):
for d from 2 to N do
if d::even then
    m:= d/2;
    Res:= Res, seq(f(n*10^m + digrev(n)), n=10^(m-1)..10^m-1);
else
    m:= (d-1)/2;
    Res:= Res, seq(seq(f(n*10^(m+1)+y*10^m+digrev(n)), y=0..9), n=10^(m-1)..10^m-1)
fi
od:
Res; # Robert Israel, Dec 25 2018

Formula

a(n) = A030668(A002113(n+1)) = A030679(n)^3. - Robert Israel, Dec 25 2018