A351714 Lucas-Niven numbers: numbers that are divisible by the number of terms in their minimal (or greedy) representation in terms of the Lucas numbers (A130310).

1, 2, 3, 4, 6, 7, 8, 10, 11, 12, 14, 18, 20, 22, 24, 27, 29, 30, 32, 36, 39, 40, 42, 47, 48, 50, 54, 57, 58, 60, 64, 66, 69, 72, 76, 78, 80, 81, 84, 90, 92, 94, 96, 100, 104, 108, 120, 123, 124, 126, 129, 130, 132, 134, 135, 138, 140, 144, 152, 153, 156, 159, 160

Offset

1,2

Comments

Numbers k such that A116543(k) | k.

Links

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

Example

6 is a term since its minimal Lucas representation, A130310(6) = 1001, has A116543(6) = 2 1's and 6 is divisible by 2.

Mathematica

lucasNivenQ[n_] := Module[{s = {}, m = n, k = 1}, While[m > 0, If[m == 1, k = 1; AppendTo[s, k]; m = 0, If[m == 2, k = 0; AppendTo[s, k]; m = 0, While[LucasL[k] <= m, k++]; k--; AppendTo[s, k]; m -= LucasL[k]; k = 1]]]; Divisible[n, Plus @@ IntegerDigits[Total[2^s], 2]]]; Select[Range[160], lucasNivenQ]

Crossrefs

Cf. A000032, A116543, A130310.

Subsequences: A351715, A351716.

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

Sequence in context: A027564 A284941 A354767 * A248559 A186511 A066049

Adjacent sequences: A351711 A351712 A351713 * A351715 A351716 A351717

Keyword

nonn,base

Author

Amiram Eldar, Feb 17 2022

Status

approved