A342036 Palindromes of even length only using 0 or 1.

0, 11, 1001, 1111, 100001, 101101, 110011, 111111, 10000001, 10011001, 10100101, 10111101, 11000011, 11011011, 11100111, 11111111, 1000000001, 1000110001, 1001001001, 1001111001, 1010000101, 1010110101, 1011001101, 1011111101, 1100000011, 1100110011

Offset

0,2

Comments

Subsequence of A057148.

a(n) is a multiple of 11.

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = A007088(n) * 10^A070939(n) + A305989(n).

a(n) = A007088(A048701(n)). - Michel Marcus, Feb 26 2021

Example

A006995|A057148|A048701|A342036|A048700|A342040
-------+-------+-------+-------+-------+-------
     0 |     0 |     0 |     0 |       |
     1 |     1 |       |       |     1 |     1
     3 |    11 |     3 |    11 |       |
     5 |   101 |       |       |     5 |   101
     7 |   111 |       |       |     7 |   111
     9 |  1001 |     9 |  1001 |       |
    15 |  1111 |    15 |  1111 |       |
    17 | 10001 |       |       |    17 | 10001

Mathematica

Array[FromDigits@ Join[#, Reverse[#]] &@ IntegerDigits[#, 2] &, 26, 0] (* Michael De Vlieger, Feb 26 2021 *)

Prog

(Ruby)
def A(n)
  str = n.to_s(2)
  (str + str.reverse).to_i
end
def A342036(n)
  (0..n).map{|i| A(i)}
end
p A342036(30)
(Python)
def a(n): b = bin(n)[2:]; return int(b+b[::-1])
print([a(n) for n in range(27)]) # Michael S. Branicky, Feb 26 2021

Crossrefs

Cf. A006995, A007088, A048701, A057148, A070939, A305989, A342040.

Sequence in context: A278753 A266670 A272654 * A004656 A143016 A152577

Adjacent sequences: A342033 A342034 A342035 * A342037 A342038 A342039

Keyword

nonn,easy,base

Author

Seiichi Manyama, Feb 26 2021

Extensions

Offset changed to 0 by Andrey Zabolotskiy, Dec 26 2022

Status

approved