A356899 Nonnegative numbers whose minimal and maximal tribonacci representations are the same.

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, 35, 36, 39, 40, 41, 42, 43, 52, 53, 54, 55, 56, 59, 60, 61, 62, 63, 65, 66, 67, 72, 73, 74, 76, 77, 78, 79, 80, 96, 97, 98, 99, 100, 102, 103, 104, 109, 110, 111, 113

Offset: 1

Author

Amiram Eldar, Sep 03 2022

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A278038, A352103.

A089068 is a subsequence.

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

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