A372729 - OEIS

A372729

a(n) is the smallest k such that the first n digits of Fibonacci(k) are the reverse of its last n digits.

0, 10, 317, 1235, 28898, 120742, 1411753, 201095722, 306312948, 12306316582, 32679761048, 806327047899, 9600042921304, 172192972068022

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OFFSET

1,2

COMMENTS

(Inspired by D. S. McNeil's comment at A045504 that typically a Fibonacci number can be ruled out as a possible palindrome by checking only a few digits at the start and end of the number.)

LINKS

Table of n, a(n) for n=1..14.

Kevin Ryde, C Code

EXAMPLE

a(1) = 0 (as Fibonacci(0) = 0 is the smallest Fibonacci number).

a(2) = 10 (Fibonacci(10) = 55 is the only 2-digit Fibonacci number that is palindromic, and almost certainly the only multidigit palindromic Fibonacci number; see A045504).

a(3) = 317 because Fibonacci(317) (a 66-digit number) is the smallest Fibonacci number whose first 3 digits (793) are the reverse of its last 3 digits (397).

The table below lists the first 8 terms and the corresponding Fibonacci numbers (abbreviated, for n > 2):

n a(n) Fibonacci(a(n))

- --------- -------------------

1 0 0

2 10 55

3 317 793...397

4 1235 5626...6265

5 28898 94480...08449

6 120742 172255...552271

7 1411753 3789665...5669873

8 201095722 11367389...98376311

PROG