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A288252
Positive integers n such that the Fibonacci (or Zeckendorf) representation of n^2 is a palindrome.
1
1, 2, 3, 8, 21, 38, 55, 80, 144, 168, 174, 195, 314, 377, 682, 987, 2584, 6360, 6765, 12238, 13301, 17711, 34985, 46368, 54096, 66483, 87849, 121393, 219602, 317811, 684704, 832040, 1486717, 2178309, 3325460, 3940598, 5702887, 6151102, 10008701, 14930352
OFFSET
1,2
COMMENTS
The sequence is infinite because F(2n)^2 = A049684(n) has Fibonacci (or Zeckendorf) representation (1000)^(n-1) 1.
LINKS
EXAMPLE
38 is in the sequence because 38^2 = 1444 has Fibonacci representation 101000101000101, which is a palindrome.
MAPLE
for n from 1 do
zeck := A014417(n^2) ;
if isA002113(zeck) then
printf("%d, \n", n);
end if;
end do: # R. J. Mathar, Jun 16 2017
CROSSREFS
Cf. A014417, which explains Fibonacci representation. Cf. A094202.
Sequence in context: A137652 A185381 A251608 * A122263 A132730 A004790
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Jun 07 2017
EXTENSIONS
a(35)-a(39) from Alois P. Heinz, Jun 14 2018
a(40) from Giovanni Resta, Jun 15 2018
STATUS
approved