A356897 Nonnegative numbers whose maximal tribonacci representation (A352103) ends in an odd number of 1's.

1, 5, 7, 8, 12, 18, 20, 21, 25, 27, 29, 31, 32, 36, 42, 44, 45, 49, 52, 56, 62, 64, 65, 69, 71, 73, 75, 76, 80, 86, 88, 89, 93, 95, 99, 101, 102, 106, 108, 110, 112, 113, 117, 123, 125, 126, 130, 133, 137, 143, 145, 146, 150, 152, 154, 156, 157, 161, 167, 169

Offset

1,2

Comments

Numbers k such that A356898(k) is odd.

The asymptotic density of this sequence is 1/(c+1) = 0.352201..., where c = 1.839286... (A058265) is the tribonacci constant.

Links

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

Example

   n  a(n)  A352103(n)  A356898(n)
   -  ----  ----------  ----------
   1     1           1          1
   2     5         101          1
   3     7         111          3
   4     8        1001          1
   5    12        1101          1
   6    18       10101          1
   7    20       10111          3
   8    21       11001          1
   9    25       11101          1
  10    27       11111          5

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]]; f[v_] := Module[{m = Length[v], k}, k = m; While[v[[k]] == 1, k--]; m - k]; c[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 == {}, 0, f[v[[i[[1, 1]] ;; -1]]], 10]]; Select[Range[0, 200], OddQ[c[#]] &]

Crossrefs

Complement of A356896.

Cf. A058265, A352103, A356898.

Similar sequences: A001950, A308198, A342050.

Sequence in context: A171420 A047384 A257772 * A314374 A066001 A320391

Adjacent sequences: A356894 A356895 A356896 * A356898 A356899 A356900

Keyword

nonn,base

Author

Amiram Eldar, Sep 03 2022

Status

approved