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).

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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]

Crossrefs

Cf. A352103, A352104.

Subsequences: A352108, A352109, A352110.

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

Sequence in context: A240498 A081954 A096903 * A273457 A222603 A177710

Adjacent sequences: A352104 A352105 A352106 * A352108 A352109 A352110

Keyword

nonn,base

Author

Amiram Eldar, Mar 05 2022

Status

approved