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Numbers k such that k and k+1 are both lazy-tribonacci-Niven numbers (A352107).
11

%I #9 Mar 07 2022 19:00:33

%S 1,20,39,75,115,135,155,175,176,184,204,215,264,567,684,704,725,791,

%T 846,872,1089,1104,1115,1134,1183,1184,1211,1224,1407,1575,1840,1880,

%U 2064,2075,2151,2191,2232,2259,2260,2415,2529,2583,2624,2780,2820,2848,2888,2988

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

%H Amiram Eldar, <a href="/A352108/b352108.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t 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] &]

%Y Cf. A352103, A352104.

%Y Subsequence of A352107.

%Y Subsequences: A352109, A352110.

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

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Mar 05 2022