A371805 Composite numbers k that divide A001644(k) - 1.

182, 25201, 54289, 63618, 194390, 750890, 804055, 1889041, 2487941, 3542533, 3761251, 6829689, 12032021, 12649337, 18002881

Offset: 1

Author

Robert FERREOL, Apr 06 2024

Keywords

• nonn
• more

Comments

If k is prime, k divides A001644(k) - 1; and since A001644(k) satisfies a tribonacci recurrence, these numbers could be called tribonacci pseudoprimes.

Examples

			(A001644(182)-1)/182 = 8056145960961609628091266244940745410646318417.
		

Crossrefs

Cf. A001644.

Cf. A005845 (composite k that divide Lucas(k) - 1).

Cf. A013998 (composite k that divide Perrin(k) - 1).

Programs

Maple

A001644:=proc(n) option remember: if n=0 then 3 elif n=1 then 1 elif n=2 then 3 else A001644(n-1)+A001644(n-2)+A001644(n-3) fi end:
test:=n->A001644(n) mod n = 1:select(test and not isprime, [seq(n, n=1..100000)]);

Mathematica

seq[kmax_] := Module[{x = 1, y = 3, z = 7, s = {}, t}, Do[t = x + y + z; If[Mod[t, k] == 1 && CompositeQ[k], AppendTo[s, k]]; x = y; y = z; z = t, {k, 4, kmax}]; s]; seq[200000] (* Amiram Eldar, Apr 06 2024 *)

Python

from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    t0, t1, t2 = 3, 1, 3
    for k in count(1):
        t0, t1, t2 = t1, t2, t0+t1+t2
        if k > 1 and not isprime(k) and (t0-1)%k == 0:
            yield k
print(list(islice(agen(), 5))) # Michael S. Branicky, Apr 07 2024

Extensions

a(13)-a(15) from Amiram Eldar, Apr 07 2024