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

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SubsequenceSubsequences: A000079, A000295, A144414.

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.

allocated for Amiram EldarNumbers whose skew binary representation (A169683) is palindromic.

0, 1, 2, 4, 8, 11, 16, 26, 32, 39, 50, 57, 64, 86, 98, 120, 128, 143, 166, 181, 194, 209, 232, 247, 256, 302, 326, 372, 386, 432, 456, 502, 512, 543, 590, 621, 646, 677, 724, 755, 770, 801, 848, 879, 904, 935, 982, 1013, 1024, 1118, 1166, 1260, 1286, 1380, 1428

1,3

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.

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.

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.

The first 10 terms are:

n a(n) A169683(a(n))

-- ---- -------------

1 0 0

2 1 1

3 2 2

4 4 11

5 8 101

6 11 111

7 16 1001

8 26 1111

9 32 10001

10 39 10101

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 *)

Cf. A169683.

Subsequence: A000079, A000295, A144414.

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

allocated

nonn,base

Amiram Eldar, Jun 10 2022

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editing