A045504 Palindromic Fibonacci numbers.

0, 1, 1, 2, 3, 5, 8, 55

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• base
• more
• hard

Comments

Also, Luca proved that 0,1,1,2,3,5,8,55 are the only Fibonacci numbers containing a single distinct digit.

Probably 55 is the last term. Indices of the palindromic Fibonacci numbers are 0,1,2,3,4,5,6,10. - Robert G. Wilson v, Jun 29 2007

There are no further terms up to Fibonacci(10^8), found in 36 processor minutes. Note that one typically only needs to check a few digits at the start and the end to rule out being a palindrome. - D. S. McNeil, Dec 30 2010

Examples

			55 is the 10th Fibonacci number and it is also palindromic in base 10.
		

Links

• Florian Luca, Fibonacci and Lucas numbers with only one distinct digit, Portugal. Math. (2000) 57 (2), 243-254.

Crossrefs

Cf. A000045, A002113, A372729.

Programs

Magma

IsPalindromic := func;  [Fn:n in[1..10^4]|IsPalindromic(Fn)where Fn is Fibonacci(n)]; /* Jason Kimberley, Dec 29 2010 */

Mathematica

fQ[n_] := Block[{id = IntegerDigits@ Fibonacci@ n}, id == Reverse@ id]; lst = {}; Do[ If[ fQ@n, AppendTo[lst, n]], {n, 0, 1000}]; Fibonacci /@ lst (* Robert G. Wilson v, Jun 29 2007 *)
SelectFibonacciPalindrome[n_] := Select[Table[Fibonacci[i], {i, 0, n}], PalindromeQ]; SelectFibonacciPalindrome[1000] (* Navvye Anand, May 11 2024 *)

PARI

ispal(n)=my(d=digits(n));for(i=1,#d\2,if(d[i]!=d[#d+1-i], return(0))); 1
is(n)=my(k=n^2); k+=(k+1)<<2; n >= 0 && (issquare(k) || issquare(k-8)) && ispal(n) \\ Charles R Greathouse IV, Feb 04 2013

Extensions

Edited by Max Alekseyev, Oct 09 2009