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A352719
Indices k of tribonacci numbers T(k) such that T(k+1) - (tribonacci constant)*T(k) is nonnegative.
1
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.
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.
Sequence in context: A330143 A140758 A292987 * A187580 A094178 A085795
KEYWORD
nonn
AUTHOR
Tanya Khovanova and the MIT PRIMES STEP Senior group, Apr 01 2022
STATUS
approved