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

1602, 218349, 296469, 1213749, 1291869, 1896630, 1952070, 2153709, 2399550, 3149109, 3753870, 3809310, 3983229, 4226208, 4256790, 4449288, 4711482, 5707897, 5727708, 6141750, 6589230, 6969429, 7205757, 7229208, 7276143, 7292943, 7454710, 7752588, 7937109, 8877069

Offset

1,1

Comments

Conjecture: There are no runs of 5 consecutive tribonacci-Niven numbers (checked up to 10^10).

Links

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

Example

1602 is a term since 1602, 1603, 1604 and 1605 are all divisible by the number of terms in their minimal tribonacci representation:
     k    A278038(k)  A278043(k)  k/A278043(k)
  --------------------------------------------
  1602  110100011010           6           267
  1603  110100011011           7           229
  1604  110100100000           4           401
  1605  110100100001           5           321

Mathematica

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]

Crossrefs

Cf. A278038, A278043.

Subsequence of A352089, A352090 and A352091.

Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344.

Sequence in context: A031538 A202774 A293370 * A252439 A224949 A171466

Adjacent sequences: A352089 A352090 A352091 * A352093 A352094 A352095

Keyword

nonn,base

Author

Amiram Eldar, Mar 04 2022

Status

approved