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A030678
Smallest nontrivial extension of n-th palindrome which is a cube.
2
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
1,1
LINKS
FORMULA
a(n) = A030668(A002113(n+1)) = A030679(n)^3. - Robert Israel, Dec 25 2018
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
CROSSREFS
KEYWORD
nonn,base
STATUS
approved