A354884 - OEIS

%I #11 Jun 12 2022 02:57:38

%S 0,1,2,4,8,11,16,26,32,39,50,57,64,86,98,120,128,143,166,181,194,209,

%T 232,247,256,302,326,372,386,432,456,502,512,543,590,621,646,677,724,

%U 755,770,801,848,879,904,935,982,1013,1024,1118,1166,1260,1286,1380,1428

%N Numbers whose skew binary representation (A169683) is palindromic.

%C The sequence of powers of 2 (A000079) is a subsequence since A169683(1) = 1, A169683(2) = 2, and for n > 2 A169683(2^n) = 10..01 with n-1 0's between the two 1's.

%C A000295 is a subsequence since A169683(A000295(0)) = A169683(A000295(1)) = 0 and for n>1 A169683(A000295(n)) is a repunit with n-1 1's.

%C A144414 is a subsequence since A169683(A144414(1)) = 1 and for n>1 A169683(A144414(n)) = 1010..01 with n-1 0's interleaved with n 1's.

%H Amiram Eldar, <a href="/A354884/b354884.txt">Table of n, a(n) for n = 1..10000</a>

%e The first 10 terms are:

%e    n  a(n)  A169683(a(n))

%e   --  ----  -------------

%e    1    0               0

%e    2    1               1

%e    3    2               2

%e    4    4              11

%e    5    8             101

%e    6   11             111

%e    7   16            1001

%e    8   26            1111

%e    9   32           10001

%e   10   39           10101

%t f[0] = 0; f[n_] := Module[{m = Floor@Log2[n + 1], d = n, pos}, Reap[While[m > 0, pos = 2^m - 1; Sow@Floor[d/pos]; d = Mod[d, pos]; --m;]][[2, 1]] // FromDigits]; Select[Range[0, 15000], PalindromeQ[f[#]] &] (* after _N. J. A. Sloane_ at A169683 *)

%Y Cf. A169683.

%Y Subsequences: A000079, A000295, A144414.

%Y Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712, A351717, A352087, A352105, A352319, A352341.

%K nonn,base

%O 1,3

%A _Amiram Eldar_, Jun 10 2022