cp's OEIS Frontend

A372729 a(n) is the smallest k such that the first n digits of Fibonacci(k) are the reverse of its last n digits.

%I A372729 #10 Aug 22 2024 05:29:39
%S A372729 0,10,317,1235,28898,120742,1411753,201095722,306312948,12306316582,
%T A372729 32679761048,806327047899,9600042921304,172192972068022
%N A372729 a(n) is the smallest k such that the first n digits of Fibonacci(k) are the reverse of its last n digits.
%C A372729 (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.)
%H A372729 Kevin Ryde, <a href="/A372729/a372729.c.txt">C Code</a>
%e A372729 a(1) = 0 (as Fibonacci(0) = 0 is the smallest Fibonacci number).
%e A372729 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).
%e A372729 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).
%e A372729 The table below lists the first 8 terms and the corresponding Fibonacci numbers (abbreviated, for n > 2):
%e A372729 .
%e A372729   n       a(n)    Fibonacci(a(n))
%e A372729   -  ---------  -------------------
%e A372729   1          0           0
%e A372729   2         10          55
%e A372729   3        317       793...397
%e A372729   4       1235      5626...6265
%e A372729   5      28898     94480...08449
%e A372729   6     120742    172255...552271
%e A372729   7    1411753   3789665...5669873
%e A372729   8  201095722  11367389...98376311
%o A372729 (C) /* See links. */
%Y A372729 Cf. A000045, A002113, A045504.
%K A372729 nonn,base,hard,more
%O A372729 1,2
%A A372729 _Jon E. Schoenfield_, May 11 2024
%E A372729 a(9)-a(14) from _Kevin Ryde_, Aug 22 2024