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A352092 Starts of runs of 4 consecutive tribonacci-Niven numbers (A352089).

%I A352092 #8 Mar 05 2022 04:02:24
%S A352092 1602,218349,296469,1213749,1291869,1896630,1952070,2153709,2399550,
%T A352092 3149109,3753870,3809310,3983229,4226208,4256790,4449288,4711482,
%U A352092 5707897,5727708,6141750,6589230,6969429,7205757,7229208,7276143,7292943,7454710,7752588,7937109,8877069
%N A352092 Starts of runs of 4 consecutive tribonacci-Niven numbers (A352089).
%C A352092 Conjecture: There are no runs of 5 consecutive tribonacci-Niven numbers (checked up to 10^10).
%H A352092 Amiram Eldar, <a href="/A352092/b352092.txt">Table of n, a(n) for n = 1..10000</a>
%e A352092 1602 is a term since 1602, 1603, 1604 and 1605 are all divisible by the number of terms in their minimal tribonacci representation:
%e A352092      k    A278038(k)  A278043(k)  k/A278043(k)
%e A352092   --------------------------------------------
%e A352092   1602  110100011010           6           267
%e A352092   1603  110100011011           7           229
%e A352092   1604  110100100000           4           401
%e A352092   1605  110100100001           5           321
%t A352092 t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; triboNivenQ[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]; Divisible[n, DigitCount[Total[2^(s - 1)], 2, 1]]]; seq[count_, nConsec_] := Module[{tri = triboNivenQ /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ tri, c++; AppendTo[s, k - nConsec]]; tri = Join[Rest[tri], {triboNivenQ[k]}]; k++]; s]; seq[6, 4]
%Y A352092 Cf. A278038, A278043.
%Y A352092 Subsequence of A352089, A352090 and A352091.
%Y A352092 Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344.
%K A352092 nonn,base
%O A352092 1,1
%A A352092 _Amiram Eldar_, Mar 04 2022