A351720 Numbers k such that k and k + 1 are both lazy-Lucas-Niven numbers (A351719).

1, 175, 216, 399, 656, 729, 737, 759, 1000, 1991, 2716, 2820, 2925, 3970, 4068, 4224, 4499, 4641, 5316, 5819, 6565, 6720, 6902, 7890, 9840, 10751, 11843, 12194, 12614, 13034, 13272, 14909, 15483, 15495, 16029, 17234, 17444, 17731, 18074, 18885, 19305, 19669, 20188

Offset

1,2

Links

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

Example

175 is a term since 175 and 176 are both lazy-Lucas-Niven numbers: the maximal Lucas representation of 175, A130311(175) = 1110110101, has 7 1's and 175 is divisible by 5, and the maximal Lucas representation of 176, A130311(7) = 1110110111, has 8 1's and 176 is divisible by 8.

Mathematica

lazy = Select[IntegerDigits[Range[10^6], 2], SequenceCount[#, {0, 0}] == 0 &]; t = Total[#*Reverse@LucasL[Range[0, Length[#] - 1]]] & /@ lazy; s = FromDigits /@ lazy[[TakeWhile[Flatten[FirstPosition[t, #] & /@ Range[Max[t]]], NumberQ]]]; SequencePosition[Divisible[Range[Length[s]], Plus @@@ IntegerDigits[s]], {True, True}][[;; , 1]]

Crossrefs

Cf. A000032, A130311, A131343.

Subsequence of A351719.

A351721 is a subsequence.

Similar sequences: A330927, A328205, A328209, A328213, A330931, A331086, A333427, A334309, A331820, A342427, A344342, A351715.

Sequence in context: A245035 A102538 A045145 * A015806 A369954 A109836

Adjacent sequences: A351717 A351718 A351719 * A351721 A351722 A351723

Keyword

nonn,base

Author

Amiram Eldar, Feb 17 2022

Status

approved