OFFSET
1,3
COMMENTS
A027084(n) is a term since its maximal tribonacci representation is n-1 1's and no 0's.
The pairs {A008937(3*k+1)-1, A008937(3*k+1)} = {0, 1}, {7, 8}, {51, 52}, ... are consecutive terms in this sequence: the maximal tribonacci representation of A008937(3*k+1)-1 is 3*k 1's and no 0's (except for k=0 where the representation is 0), and the maximal tribonacci representation of A008937(3*k+1) is of the form 100100...1001 with k blocks of 100 followed by a 1 at the end.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
The first 10 terms are:
n a(n) A352103(a(n))
-- ---- -------------
1 0 0
2 1 1
3 3 11
4 5 101
5 7 111
6 8 1001
7 14 1111
8 18 10101
9 23 11011
10 27 11111
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]]; q[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 == {}, True, PalindromeQ[FromDigits[v[[i[[1, 1]] ;; -1]]]]]]; Select[Range[0, 1000], q]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Mar 05 2022
STATUS
approved