OFFSET
1,1
COMMENTS
Conjecture: There are no runs of 5 consecutive tribonacci-Niven numbers (checked up to 10^10).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
1602 is a term since 1602, 1603, 1604 and 1605 are all divisible by the number of terms in their minimal tribonacci representation:
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1602 110100011010 6 267
1603 110100011011 7 229
1604 110100100000 4 401
1605 110100100001 5 321
MATHEMATICA
t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; triboNivenQ[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[t[k] <= m, k++]; k--; AppendTo[s, k]; m -= t[k]; k = 1]; Divisible[n, DigitCount[Total[2^(s - 1)], 2, 1]]]; seq[count_, nConsec_] := Module[{tri = triboNivenQ /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ tri, c++; AppendTo[s, k - nConsec]]; tri = Join[Rest[tri], {triboNivenQ[k]}]; k++]; s]; seq[6, 4]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Mar 04 2022
STATUS
approved