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A352108
Numbers k such that k and k+1 are both lazy-tribonacci-Niven numbers (A352107).
11
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
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
Subsequence of A352107.
Subsequences: A352109, A352110.
Sequence in context: A054288 A238245 A215144 * A333234 A040380 A154044
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Mar 05 2022
STATUS
approved