1,1

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.

a(1) = A128288(74) = 1853 = 17*109.

a(2) = 9701 = 89*109.

a(3) = 10877 = 73*149.

a(4) = 17261 = 41*421.

a(5) = 23323 = 83*281.

Do[ f = Mod[ Fibonacci[3n], 3n ]; If[ !PrimeQ[n] && f == 3n-2, Print[ {n, FactorInteger[n]} ]], {n, 1, 25000} ]

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.

Sequence in context: A031631 A031541 A031721 this_sequence A023044 A051355 A064978

Adjacent sequences: A128286 A128287 A128288 this_sequence A128290 A128291 A128292

hard,more,nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 24 2007

Two more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 08 2007