%I A128289
%S A128289 1853,9701,10877,17261,23323,27403,75077,80189
%N A128289 Composite terms in A128288(n) = A023163(n)/3 for n>1.
%C A128289 3 divides A023163(n) for n>1. A023163(n) are the numbers n such that 
               Fibonacci(n) == -2 (mod n). Almost all terms of A128288(n) are prime 
               that belong to A003631 = {2, 3, 7, 13, 17, 23, 37, 43, 47, 53, 67, 
               73, 83, 97} Primes congruent to {2, 3} mod 5; that are also the primes 
               p that divide Fibonacci(p+1). a(3) = 10877 = 73*149 belong to A069107 
               Composite n such that n divides F(n+1) where F(k) are the Fibonacci 
               numbers. a(3) = 10877 and a(4) = 17261 belong to A094395 Odd composite 
               n such that n divides Fibonacci(n) + 1.
%e A128289 a(1) = A128288(74) = 1853 = 17*109.
%e A128289 a(2) = 9701 = 89*109.
%e A128289 a(3) = 10877 = 73*149.
%e A128289 a(4) = 17261 = 41*421.
%e A128289 a(5) = 23323 = 83*281.
%t A128289 Do[ f = Mod[ Fibonacci[3n], 3n ]; If[ !PrimeQ[n] && f == 3n-2, Print[ 
               {n, FactorInteger[n]} ]], {n,1,25000} ]
%Y A128289 Cf. A128288, A002708, A023172, A023173, A023162, A023163 = numbers n 
               such that Fib(n) == -2 (mod n). Cf. A003631, A069107, A094413, A094395 
               = Odd composite n such that n divides Fibonacci(n) + 1.
%Y A128289 Sequence in context: A031631 A031541 A031721 this_sequence A023044 A051355 
               A064978
%Y A128289 Adjacent sequences: A128286 A128287 A128288 this_sequence A128290 A128291 
               A128292
%K A128289 hard,more,nonn
%O A128289 1,1
%A A128289 Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 24 2007
%E A128289 Two more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 
               08 2007