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%I #7 Feb 21 2022 02:30:32
%S 1,2,3,6,7,10,11,29,39,47,57,80,123,129,134,152,159,170,176,199,206,
%T 245,279,326,384,387,398,404,521,531,543,560,579,615,644,651,684,755,
%U 843,849,854,872,879,890,896,944,1024,1052,1064,1070,1071,1095,1350,1382
%N Numbers k such that k and k + 1 are both Lucas-Niven numbers (A351714).
%H Amiram Eldar, <a href="/A351715/b351715.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t 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} &]
%Y Subsequence of A351714.
%Y A351716 is a subsequence.
%Y Similar sequences: A330927, A328205, A328209, A328213, A330931, A331086, A333427, A334309, A331820, A342427, A344342, A351720.
%K nonn,base
%O 1,2
%A _Amiram Eldar_, Feb 17 2022
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