A128288 -id:A128288 - cp's OEIS frontend

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

Alexander Adamchuk, Feb 24 2007

nonn

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.

			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.

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

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.

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

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

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

A351337 Composite terms in A270951.

Original entry on oeis.org

169, 385, 961, 1121, 3741, 3781, 4795, 4901, 6061, 6265, 6441, 6601, 6895, 6931, 7801, 8119, 9809, 9881, 10945, 13981, 14111, 15841, 18241, 18721, 19097, 20833, 23829, 24727, 29953, 30381, 30889, 31417, 34561, 37345, 38081, 40391, 42127, 45961, 47321, 49105

Offset: 1

Bill McEachen, Feb 08 2022

nonn

The sequence appears to have no intersection with A128288.

Intersection of A002808 and A270951.

Cf. A128288.

q[n_] := CompositeQ[n] && Divisible[Fibonacci[n - 1, 2], n]; Select[Range[50000], q] (* Amiram Eldar, Feb 09 2022 *)

a000129(n) = ([2, 1; 1, 0]^n)[2, 1];
is(n) = (n>1) && !isprime(n) && (Mod(a000129(n-1), n) == 0); \\ Michel Marcus, Feb 09 2022; after A270951

cp's OEIS Frontend

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

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