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A376029
Tribonacci-Niven numbers (A352089) with a record gap to the next tribonacci-Niven number.
2
1, 2, 8, 48, 140, 244, 620, 705, 1395, 6210, 9656, 14322, 52024, 88128, 95589, 119440, 151130, 325105, 407128, 472790, 520971, 686103, 4456608, 7066416, 13207389, 15488160, 23381160, 42317212, 49496700, 53564016, 128163495, 165750096, 387900480, 421730960, 485880806
OFFSET
1,2
COMMENTS
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.
REFERENCES
Andrew B. Ray, On the natural density of the k-Zeckendorf Niven numbers, Ph.D. dissertation, Central Missouri State University, 2005.
LINKS
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.
EXAMPLE
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.
MATHEMATICA
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]
CROSSREFS
Similar sequences: A337076, A337077, A347495, A347496, A376028.
Sequence in context: A003032 A193944 A058928 * A228288 A356346 A292277
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Sep 06 2024
STATUS
approved