%I #20 Sep 12 2022 03:51:02
%S 25,60,120,125,180,240,300,323,360,377,480,540,600,625,660,720,840,
%T 900,960,1080,1200,1320,1440,1500,1620,1680,1800,1860,1891,1920,1980,
%U 2160,2400,2460,2520,2640,2700,2760,2880,3000,3060,3125,3240,3300,3360,3420
%N Composite integers k satisfying F_k-(k/5) == 0 (mod k), where F_k is the k-th Fibonacci number and (k/5) is the Kronecker symbol.
%C Sequence resembles A090820, although they are not identical.
%H Amiram Eldar, <a href="/A241505/b241505.txt">Table of n, a(n) for n = 1..10000</a>
%H Z. H. Sun and Z. W. Sun, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa60/aa6046.pdf">Fibonacci numbers and Fermat's last theorem</a>, Acta Arithmetica 60(4) (1992), 371-388.
%t Select[Range[2, 5000], ! PrimeQ[#] && Mod[Fibonacci[# - JacobiSymbol[#, 5]], #] == 0 &] (* _Jean-François Alcover_, Apr 24 2014 *)
%o (PARI) forcomposite(n=2, 1e4, if(Mod(fibonacci(n-kronecker(n, 5)), n)==0, print1(n, ", ")))
%Y Cf. A000045, A090820.
%K nonn
%O 1,1
%A _Felix Fröhlich_, Apr 24 2014