A352748 - OEIS

%I #12 Apr 06 2022 08:47:13

%S 2,5,8,11,13,14,16,17,19,20,22,23,25,28,31,34,37,39,40,42,43,45,46,48,

%T 49,51,54,57,60,63,65,66,68,69,71,72,74,75,77,80,83,86,89,91,92,94,95,

%U 97,98

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

%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(5) = 4 and T(6) = 7. Therefore, T(6) - (tribonacci constant)*T(5) equals approximately -0.356 < 0. Thus, index 5 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 A352719.

%Y Cf. A000073, A058265.

%K nonn

%O 1,1

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