1,2

The corresponding record gaps are 1, 2, 4, 8, 9, 12, 15, 20, ... (see the link for more values).

Ray (2005) and Ray and Cooper (2006) proved that the asymptotic density of the tribonacci-Niven numbers is 0. Therefore, this sequence is infinite.

Andrew B. Ray, On the natural density of the k-Zeckendorf Niven numbers, Ph.D. dissertation, Central Missouri State University, 2005.

Amiram Eldar, Table of n, a(n) for n = 1..42

Amiram Eldar, Table of n, a(n), gap(n) for n = 1..42

Andrew Ray and Curtis Cooper, On the natural density of the k-Zeckendorf Niven numbers, J. Inst. Math. Comput. Sci. Math., Vol. 19 (2006), pp. 83-98.

The first 7 tribonacci-Niven numbers are 1, 2, 4, 6, 7, 8 and 12. The gaps between them are 1, 2, 2, 1, 1 and 4, and the record gaps, 1, 2 and 4 occur after 1, 2 and 8, the first 3 terms of this sequence.

t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; tnQ[n_] := Module[{s = 0, m = n, k}, While[m > 0, k = 1; While[t[k] <= m, k++]; k--; s++; m -= t[k]; k = 1]; Divisible[n, s]]; seq[kmax_] := Module[{gapmax = 0, gap, k1 = 1, s = {}}, Do[If[tnQ[k], gap = k - k1; If[gap > gapmax, gapmax = gap; AppendTo[s, k1]]; k1 = k], {k, 2, kmax}]; s]; seq[10^4]

Cf. A352089, A352090.

Similar sequences: A337076, A337077, A347495, A347496, A376028.

Sequence in context: A003032 A193944 A058928 * A228288 A392046 A356346

Adjacent sequences: A376026 A376027 A376028 * A376030 A376031 A376032

nonn,base

Amiram Eldar, Sep 06 2024

approved