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%I #9 Mar 05 2022 04:02:20
%S 0,1,3,5,8,14,18,23,25,36,40,45,52,62,71,78,82,102,110,128,148,150,
%T 163,181,198,211,229,233,246,264,275,312,326,360,397,411,426,463,477,
%U 505,529,562,593,617,650,658,682,715,746,770,781,805,838,869,893,926,928
%N Numbers whose minimal (or greedy) tribonacci representation (A278038) is palindromic.
%C A000073(n) + 1 is a term for n>=4, since its minimal tribonacci representation is 10...01 with n-4 0's between the two 1's.
%H Amiram Eldar, <a href="/A352087/b352087.txt">Table of n, a(n) for n = 1..10000</a>
%e The first 10 terms are:
%e n a(n) A278038(a(n))
%e -----------------------
%e 1 0 0
%e 2 1 1
%e 3 3 11
%e 4 5 101
%e 5 8 1001
%e 6 14 10001
%e 7 18 10101
%e 8 23 11011
%e 9 25 100001
%e 10 36 101101
%t t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; q[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]; PalindromeQ[FromDigits @ IntegerDigits[Total[2^(s - 1)], 2]]]; Select[Range[0, 1000], q]
%Y Cf. A000073, A278038.
%Y Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712, A351717.
%K nonn,base
%O 1,3
%A _Amiram Eldar_, Mar 04 2022
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