%I #6 May 21 2024 05:28:01

%S 1,3,217,13343,549333,1387663,9356863,22119541

%N Numbers k that divide the k-th term of the tribonacci sequence A000213.

%C Numbers k such that k | A000213(k).

%e 3 is a term since A000213(3) = 3 is divisible by 3.

%t With[{m = 15000}, Position[LinearRecurrence[{1, 1, 1}, {1, 1, 3}, m]/Range[m], _?IntegerQ] // Flatten]

%o (PARI) lista(kmax) = {my(t0 = 1, t1 = 1, t2 = 1, t3); print1("1, "); for(k = 3, kmax, t3 = t0 + t1 + t2; if(!(t3 % k), print1(k, ", ")); t0 = t1; t1 = t2; t2 = t3);}

%Y Cf. A000213.

%Y Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci A000073), A246692 (Pell), A266969 (Motzkin).

%K nonn,more

%O 1,2

%A _Amiram Eldar_, May 21 2024