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A352107
Lazy-tribonacci-Niven numbers: numbers that are divisible by the number of terms in their maximal (or lazy) representation in terms of the tribonacci numbers (A352103).
11
1, 2, 4, 6, 8, 12, 18, 20, 21, 24, 28, 30, 33, 36, 39, 40, 48, 50, 56, 60, 68, 70, 72, 75, 76, 80, 90, 96, 100, 108, 115, 116, 120, 135, 136, 140, 150, 155, 156, 160, 162, 168, 175, 176, 177, 180, 184, 185, 188, 195, 198, 204, 205, 208, 215, 216, 225, 231, 260
OFFSET
1,2
COMMENTS
Numbers k such that A352104(k) | k.
LINKS
EXAMPLE
6 is a term since its maximal tribonacci representation, A352103(6) = 110, has A352104(6) = 2 1's and 6 is divisible by 2.
MATHEMATICA
t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; trib[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]; IntegerDigits[Total[2^(s - 1)], 2]]; q[n_] := Module[{v = trib[n]}, nv = Length[v]; i = 1; While[i <= nv - 3, If[v[[i ;; i + 3]] == {1, 0, 0, 0}, v[[i ;; i + 3]] = {0, 1, 1, 1}; If[i > 3, i -= 4]]; i++]; i = Position[v, _?(# > 0 &)]; If[i == {}, False, Divisible[n, Total[v[[i[[1, 1]] ;; -1]]]]]]; Select[Range[300], q]
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Mar 05 2022
STATUS
approved