A352108 Numbers k such that k and k+1 are both lazy-tribonacci-Niven numbers (A352107).

1, 20, 39, 75, 115, 135, 155, 175, 176, 184, 204, 215, 264, 567, 684, 704, 725, 791, 846, 872, 1089, 1104, 1115, 1134, 1183, 1184, 1211, 1224, 1407, 1575, 1840, 1880, 2064, 2075, 2151, 2191, 2232, 2259, 2260, 2415, 2529, 2583, 2624, 2780, 2820, 2848, 2888, 2988

Offset

1,2

Links

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

Example

20 is a term since 20 and 21 are both lazy-tribonacci-Niven numbers: the maximal tribonacci representation of 20, A352103(20) = 10111, has 4 1's and 20 is divisible by 4, and the maximal tribonacci representation of 21, A352103(20) = 11001, has 3 1's and 21 is divisible by 3.

Mathematica

t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; trib[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[t[k] <= m, k++]; k--; AppendTo[s, k]; m -= t[k]; k = 1]; IntegerDigits[Total[2^(s - 1)], 2]]; q[n_] := Module[{v = trib[n]}, nv = Length[v]; i = 1; While[i <= nv - 3, If[v[[i ;; i + 3]] == {1, 0, 0, 0}, v[[i ;; i + 3]] = {0, 1, 1, 1}; If[i > 3, i -= 4]]; i++]; i = Position[v, _?(# > 0 &)]; If[i == {}, False, Divisible[n, Total[v[[i[[1, 1]] ;; -1]]]]]]; Select[Range[3000], q[#] && q[# + 1] &]

Crossrefs

Cf. A352103, A352104.

Subsequence of A352107.

Subsequences: A352109, A352110.

Similar sequences: A330927, A328205, A328209, A328213, A330931, A331086, A333427, A334309, A331820, A342427, A344342, A351715, A351720, A352090.

Sequence in context: A054288 A238245 A215144 * A333234 A040380 A154044

Adjacent sequences: A352105 A352106 A352107 * A352109 A352110 A352111

Keyword

nonn,base

Author

Amiram Eldar, Mar 05 2022

Status

approved