%I #8 Sep 05 2022 05:24:42

%S 0,1,2,3,4,5,6,8,9,10,11,12,15,16,17,18,19,21,22,23,28,29,30,32,33,34,

%T 35,36,39,40,41,42,43,52,53,54,55,56,59,60,61,62,63,65,66,67,72,73,74,

%U 76,77,78,79,80,96,97,98,99,100,102,103,104,109,110,111,113

%N Nonnegative numbers whose minimal and maximal tribonacci representations are the same.

%H Amiram Eldar, <a href="/A356899/b356899.txt">Table of n, a(n) for n = 1..10000</a>

%t t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3];

%t 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]];

%t tribmin[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]; FromDigits@IntegerDigits[Total[2^(s - 1)], 2]];

%t tribmax[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, FromDigits[v[[i[[1, 1]] ;; -1]]]]];

%t Select[Range[0, 150], tribmin[#] == tribmax[#] &]

%Y Cf. A278038, A352103.

%Y A089068 is a subsequence.

%Y Similar sequence: A000071 (numbers whose Zeckendorf and dual Zeckendorf representations are the same).

%K nonn,base

%O 1,3

%A _Amiram Eldar_, Sep 03 2022