A045504 Palindromic Fibonacci numbers.

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

Offset

1,4

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]

Links

Table of n, a(n) for n=1..8.

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

Example

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

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 *)

Prog

(Magma) IsPalindromic := func<Fn|forall{i:i in[1..d div 2]|digit_seq[i]eq digit_seq[d+1-i]}where d is #digit_seq where digit_seq is IntegerToString(Fn)>;  [Fn:n in[1..10^4]|IsPalindromic(Fn)where Fn is Fibonacci(n)]; /* Jason Kimberley */
(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

Crossrefs

Sequence in context: A061249 A042237 A042937 * A068500 A272623 A042667

Adjacent sequences: A045501 A045502 A045503 * A045505 A045506 A045507

Keyword

nonn,base,more,hard

Author

Jeff Burch

Extensions

Edited by Max Alekseyev, Oct 09 2009

Status

approved