A352719 - OEIS

%I #39 Apr 07 2022 10:50:48

%S 0,1,3,4,6,7,9,10,12,15,18,21,24,26,27,29,30,32,33,35,36,38,41,44,47,

%T 50,52,53,55,56,58,59,61,62,64,67,70,73,76,78,79,81,82,84,85,87,88,90,

%U 93,96,99

%N Indices k of tribonacci numbers T(k) such that T(k+1) - (tribonacci constant)*T(k) is nonnegative.

%C The tribonacci constant, which is approximately 1.839, is described in A058265. The tribonacci constant is the only real solution to the characteristic equation (x^3 = x^2+x+1) for the tribonacci sequence. It describes the asymptotic growth of the tribonacci sequence.

%C The sequence doesn't contain three consecutive numbers. Also, the difference between two consecutive numbers is never more than 3.

%e T(6) = 7 and T(7) = 13. Therefore, T(7) - (tribonacci constant)*T(6) equals approximately 0.127 > 0. Thus, index 6 is in this sequence.

%o (PARI) T(n) = ([0, 1, 0; 0, 0, 1; 1, 1, 1]^n)[1, 3]; \\ A000073

%o t = (1/3)*(1+(19+3*sqrt(33))^(1/3)+(19-3*sqrt(33))^(1/3)); \\ A058265

%o isok(k) = T(k+1) >= t*T(k); \\ _Michel Marcus_, Apr 06 2022

%Y Complement of A352748.

%Y Cf. A000073, A058265.

%K nonn

%O 1,3

%A _Tanya Khovanova_ and the MIT PRIMES STEP Senior group, Apr 01 2022