A128289 Composite terms in A128288(n) = A023163(n)/3 for n>1.

1853, 9701, 10877, 17261, 23323, 27403, 75077, 80189, 113573, 120581, 161027, 162133, 163059, 196877, 213749, 291941, 361397, 400987, 427549, 482677, 635627, 667589, 941291, 1030373, 1033997, 1140701, 1196061, 1256293, 1751747, 1816363, 1842581, 2288453, 2662277

Offset: 1

Author

Alexander Adamchuk, Feb 24 2007

Keywords

• nonn

Comments

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 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 belongs to A069107 Composite n such that n divides Fibonacci(n+1).

a(3) = 10877 and a(4) = 17261 belong to A094395 Odd composite n such that n divides Fibonacci(n) + 1.

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1000

Crossrefs

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.

Programs

Mathematica

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

Extensions

Two more terms from R. J. Mathar, Oct 08 2007

a(9)-a(33) from Amiram Eldar, Apr 07 2019