|
|
A352748
|
|
Indices k of tribonacci numbers T(k) such that T(k+1) - (tribonacci constant)*T(k) is negative.
|
|
1
|
|
|
2, 5, 8, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 28, 31, 34, 37, 39, 40, 42, 43, 45, 46, 48, 49, 51, 54, 57, 60, 63, 65, 66, 68, 69, 71, 72, 74, 75, 77, 80, 83, 86, 89, 91, 92, 94, 95, 97, 98
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
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
|
|
|
EXAMPLE
|
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.
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|