cp's OEIS Frontend

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

%I A371805 #25 May 03 2024 17:26:30
%S A371805 182,25201,54289,63618,194390,750890,804055,1889041,2487941,3542533,
%T A371805 3761251,6829689,12032021,12649337,18002881
%N A371805 Composite numbers k that divide A001644(k) - 1.
%C A371805 If k is prime, k divides A001644(k) - 1; and since A001644(k) satisfies a tribonacci recurrence, these numbers could be called tribonacci pseudoprimes.
%e A371805 (A001644(182)-1)/182 = 8056145960961609628091266244940745410646318417.
%p A371805 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:
%p A371805 test:=n->A001644(n) mod n = 1:select(test and not isprime, [seq(n, n=1..100000)]);
%t A371805 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 *)
%o A371805 (Python)
%o A371805 from sympy import isprime
%o A371805 from itertools import count, islice
%o A371805 def agen(): # generator of terms
%o A371805     t0, t1, t2 = 3, 1, 3
%o A371805     for k in count(1):
%o A371805         t0, t1, t2 = t1, t2, t0+t1+t2
%o A371805         if k > 1 and not isprime(k) and (t0-1)%k == 0:
%o A371805             yield k
%o A371805 print(list(islice(agen(), 5))) # _Michael S. Branicky_, Apr 07 2024
%Y A371805 Cf. A001644.
%Y A371805 Cf. A005845 (composite k that divide Lucas(k) - 1).
%Y A371805 Cf. A013998 (composite k that divide Perrin(k) - 1).
%K A371805 nonn,more
%O A371805 1,1
%A A371805 _Robert FERREOL_, Apr 06 2024
%E A371805 a(13)-a(15) from _Amiram Eldar_, Apr 07 2024