A351715 Numbers k such that k and k + 1 are both Lucas-Niven numbers (A351714).

1, 2, 3, 6, 7, 10, 11, 29, 39, 47, 57, 80, 123, 129, 134, 152, 159, 170, 176, 199, 206, 245, 279, 326, 384, 387, 398, 404, 521, 531, 543, 560, 579, 615, 644, 651, 684, 755, 843, 849, 854, 872, 879, 890, 896, 944, 1024, 1052, 1064, 1070, 1071, 1095, 1350, 1382

Offset

1,2

Links

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

Example

6 is a term since 6 and 7 are both Lucas-Niven numbers: the minimal Lucas representation of 6, A130310(6) = 1001, has 2 1's and 6 is divisible by 2, and the minimal Lucas representation of 7, A130310(7) = 10000, has one 1 and 7 is divisible by 1.

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[1400], And @@ lucasNivenQ/@{#, #+1} &]

Crossrefs

Subsequence of A351714.

A351716 is a subsequence.

Similar sequences: A330927, A328205, A328209, A328213, A330931, A331086, A333427, A334309, A331820, A342427, A344342, A351720.

Sequence in context: A030703 A305927 A271585 * A285259 A284907 A330572

Adjacent sequences: A351712 A351713 A351714 * A351716 A351717 A351718

Keyword

nonn,base

Author

Amiram Eldar, Feb 17 2022

Status

approved