A288252 Positive integers n such that the Fibonacci (or Zeckendorf) representation of n^2 is a palindrome.

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

Giovanni Resta, Table of n, a(n) for n = 1..60

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

Adjacent sequences: A288249 A288250 A288251 * A288253 A288254 A288255

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