Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #23 Jul 30 2019 15:08:39
%S 4181,5474,5777,6479,6721,10877,12958,13201,15251,17302,27071,34561,
%T 40948,41998,44099,47519,51841,54839,64079,64681,65471,67861,68251,
%U 72831,75077,78089,88198,90061,95038,96049,97921
%N Composite n coprime to 5 such that Fibonacci(n) == Legendre(n,5) (mod n).
%C If n is a prime, not 5, then Fibonacci(n) == Legendre(n,5) (mod n) (see for example G. H. Hardy and E. M. Wright, Theory of Numbers).
%H Amiram Eldar, <a href="/A049062/b049062.txt">Table of n, a(n) for n = 1..500</a>
%H Masataka Yorinaga, <a href="http://ousar.lib.okayama-u.ac.jp/ja/journal/mjou/19/1/article/33418">On a congruencial property of Fibonacci numbers (numerical experiments)</a>, Math. J. Okayama Univ. 19 (1976/77), no. 1, 5-10.
%H Masataka Yorinaga, <a href="http://ousar.lib.okayama-u.ac.jp/ja/journal/mjou/19/1/article/33420">On a congruencial property of Fibonacci numbers (considerations and remarks)</a>, Math. J. Okayama Univ. 19 (1976/77), no. 1, 11-17.
%t Select[ Range[ 2, 100000 ], ! PrimeQ[ # ] && Mod[ #, 5 ] != 0 && Mod[ Fibonacci[ # ] - JacobiSymbol[ #, 5 ], # ] == 0 & ]
%Y Cf. A090820.
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_
%E Yorinaga gives table up to 707000
%E More terms from _Eric Rowland_, Apr 29 2004
%E Definition corrected by _Eric Rowland_, Feb 24 2006