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

Author

Amiram Eldar, Sep 03 2022

Keywords

• nonn
• base

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.

Examples

			   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
		

Links

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

Crossrefs

Complement of A356896.

Cf. A058265, A352103, A356898.

Similar sequences: A001950, A308198, A342050.

Programs

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[#]] &]