A356899 - OEIS

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

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OFFSET

1,3

LINKS

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

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[#] &]

CROSSREFS

Cf. A278038, A352103.

A089068 is a subsequence.

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

Sequence in context: A157465 A257247 A269164 * A230780 A302540 A332487

Adjacent sequences: A356896 A356897 A356898 * A356900 A356901 A356902

KEYWORD

nonn,base

AUTHOR

Amiram Eldar, Sep 03 2022

STATUS

approved