A343129 - OEIS

%I #20 Dec 10 2021 22:58:09

%S 0,1,2,5,8,17,35,170,278,422,494

%N Numbers that are palindromes in base 3/2.

%C Next term >= 10^12. - _Joerg Arndt_, Apr 06 2021

%C Next term > 2^64. - _David Radcliffe_, Dec 10 2021

%H Matvey Borodin, Hannah Han, Kaylee Ji, Tanya Khovanova, Alexander Peng, David Sun, Isabel Tu, Jason Yang, William Yang, Kevin Zhang, and Kevin Zhao, <a href="https://arxiv.org/abs/1901.09818">Variants of Base 3 over 2</a>, arXiv:1901.09818 [math.NT], 2019.

%H B. Chen, R. Chen, J. Guo, S. Lee et al., <a href="http://arxiv.org/abs/1808.04304">On Base 3/2 and its sequences</a>, arXiv:1808.04304 [math.NT], 2018.

%e     0:  0

%e     1:  1

%e     2:  2

%e     5:  22

%e     8:  212

%e    17:  21012

%e    35:  212212

%e   170:  2120220212

%e   278:  21221112212

%e   422:  2101100011012

%e   494:  2120010100212

%t (* All terms <= 500: *)

%t b = {};

%t a[n_] := If[n < 1, 0, a[Quotient[n, 3] 2] 10 + Mod[n, 3]];

%t Do[If[PalindromeQ[a[n]], AppendTo[b, n], Nothing], {n, 0, 500}];

%t b

%Y Cf. A024629.

%K nonn,base,more

%O 0,3

%A _Wyatt Powers_, Apr 05 2021