A352087 - OEIS

%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