A352719 Indices k of tribonacci numbers T(k) such that T(k+1) - (tribonacci constant)*T(k) is nonnegative.

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, 50, 52, 53, 55, 56, 58, 59, 61, 62, 64, 67, 70, 73, 76, 78, 79, 81, 82, 84, 85, 87, 88, 90, 93, 96, 99

Offset

1,3

Comments

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.

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

Links

Table of n, a(n) for n=1..51.

Example

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.

Prog

(PARI) T(n) = ([0, 1, 0; 0, 0, 1; 1, 1, 1]^n)[1, 3]; \\ A000073
t = (1/3)*(1+(19+3*sqrt(33))^(1/3)+(19-3*sqrt(33))^(1/3)); \\ A058265
isok(k) = T(k+1) >= t*T(k); \\ Michel Marcus, Apr 06 2022

Crossrefs

Complement of A352748.

Cf. A000073, A058265.

Sequence in context: A330143 A140758 A292987 * A187580 A094178 A085795

Adjacent sequences: A352716 A352717 A352718 * A352720 A352721 A352722

Keyword

nonn

Author

Tanya Khovanova and the MIT PRIMES STEP Senior group, Apr 01 2022

Status

approved