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A351716
Starts of runs of 3 consecutive Lucas-Niven numbers (A351714).
13
1, 2, 6, 10, 1070, 4214, 10654, 10730, 13118, 31143, 39830, 43864, 47663, 48184, 50134, 62334, 63510, 79954, 83344, 84006, 89614, 107270, 119224, 119434, 121384, 124586, 124984, 129094, 129843, 148910, 165430, 167760, 168574, 183274, 193144, 198184, 198904, 199870
OFFSET
1,2
COMMENTS
Conjecture: 1 is the only start of a run of 4 consecutive Lucas-Niven numbers (checked up to 10^9).
LINKS
EXAMPLE
6 is a term since 6, 7 and 8 are all Lucas-Niven numbers: the minimal Lucas representation of 6, A130310(6) = 1001, has 2 1's and 6 is divisible by 2, the minimal Lucas representation of 7, A130310(7) = 10000, has one 1 and 7 is divisible by 1, and the minimal Lucas representation of 8, A130310(8) = 10010, has 2 1's and 8 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]]]; seq[count_, nConsec_] := Module[{luc = lucasNivenQ /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ luc, c++; AppendTo[s, k - nConsec]]; luc = Join[Rest[luc], {lucasNivenQ[k]}]; k++]; s]; seq[50, 3]
CROSSREFS
Subsequence of A351714 and A351715.
Sequence in context: A065799 A162582 A123098 * A136699 A033710 A243157
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Feb 17 2022
STATUS
approved