

A045504


Palindromic Fibonacci numbers.


4




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), 243254.


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<Fnforall{i:i in[1..d div 2]digit_seq[i]eq digit_seq[d+1i]}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+1i], return(0))); 1
is(n)=my(k=n^2); k+=(k+1)<<2; n >= 0 && (issquare(k)  issquare(k8)) && 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



