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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

%I #11 Mar 12 2022 12:10:57

%S 1,2,4,6,8,12,18,20,21,24,28,30,33,36,39,40,48,50,56,60,68,70,72,75,

%T 76,80,90,96,100,108,115,116,120,135,136,140,150,155,156,160,162,168,

%U 175,176,177,180,184,185,188,195,198,204,205,208,215,216,225,231,260

%N 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).

%C Numbers k such that A352104(k) | k.

%H Amiram Eldar, <a href="/A352107/b352107.txt">Table of n, a(n) for n = 1..10000</a>

%e 6 is a term since its maximal tribonacci representation, A352103(6) = 110, has A352104(6) = 2 1's and 6 is divisible by 2.

%t 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]

%Y Cf. A352103, A352104.

%Y Subsequences: A352108, A352109, A352110.

%Y Similar sequences: A005349, A049445, A064150, A064438, A064481, A118363, A328208, A328212, A331085, A333426, A342726, A334308, A331728, A342426, A344341, A351714, A351719, A352089.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Mar 05 2022