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 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 isok(k) = T(k+1) < t*T(k); \\ Michel Marcus, Apr 06 2022 CROSSREFS Complement of A352719. Cf. A000073, A058265. Sequence in context: A167409 A082406 A215938 * A007826 A108589 A292988 Adjacent sequences: A352745 A352746 A352747 * A352749 A352750 A352751 KEYWORD nonn AUTHOR Tanya Khovanova and the MIT PRIMES STEP Senior group, Apr 01 2022 STATUS approved

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Last modified February 2 03:35 EST 2023. Contains 359997 sequences. (Running on oeis4.)