A305989 -id:A305989 - cp's OEIS frontend

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

Seiichi Manyama, Feb 26 2021

Subsequence of A057148.

a(n) is a multiple of 11.

			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

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

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

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

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)

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

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

Offset changed to 0 by Andrey Zabolotskiy, Dec 26 2022

A342040 Binary palindromes of odd length.

Original entry on oeis.org

1, 101, 111, 10001, 10101, 11011, 11111, 1000001, 1001001, 1010101, 1011101, 1100011, 1101011, 1110111, 1111111, 100000001, 100010001, 100101001, 100111001, 101000101, 101010101, 101101101, 101111101, 110000011, 110010011, 110101011

Offset: 1

Seiichi Manyama, Feb 26 2021

Subsequence of A057148.

Cf. A006995, A007088, A048700, A057148, A070939, A305989, A342036.

a[1] = 1; a[n_] := FromDigits[Join[#, {Mod[n, 2]}, Reverse[#]] &@ IntegerDigits[Floor[n/2], 2]]; Array[a, 26] (* Amiram Eldar, Apr 28 2021 *)

def A342040(n):
    s = bin(n)[2:]
    return int(s+s[-2::-1]) # Chai Wah Wu, Feb 26 2021

a(n) = A007088(A048700(n)).

A342130 Decimal numbers m such that the product of the binary string of m and the binary string of m in reverse contains the binary string of m as a substring.

Original entry on oeis.org

0, 1, 2, 4, 8, 16, 27, 32, 54, 64, 108, 128, 139, 165, 256, 512, 815, 1024, 1630, 2048, 2821, 3167, 3693, 3941, 4096, 4747, 5642, 6334, 7737, 7881, 8192, 9494, 10837, 11284, 12479, 13363, 16384, 18988, 22568, 24669, 24958, 27945, 31205, 32768, 38869, 40861, 45136, 48367, 49338, 49535, 55121

Offset: 1

Scott R. Shannon, Mar 01 2021

All numbers of the form 2^k, k>=0, are in the sequence.

			8 is a term as bin(8)*reverse(bin(8)) = 100_2*1_2 = 100_2 contains '100' as a substring.
27 is a term as bin(27)*reverse(bin(27)) = 11011_2*11011_2 = 1011011001_2 contains '11011' as a substring.
108 is a term as bin(108)*reverse(bin(108)) = 1101100_2*11011_2 = 101101100100_2 contains '1101100' as a substring.
139 is a term as bin(139)*reverse(bin(139)) = 10001011_2*11010001_2 = 111000101111011_2 contains '10001011' as a substring.

Cf. A342127 (base 10), A305989, A007088, A000079, A203565, A332795.

strbin(x) = Str(fromdigits(binary(x), 10));
isok(m) = {my(p = m*fromdigits(Vecrev(binary(m)), 2)); #strsplit(strbin(p), strbin(m)) > 1;} \\ Michel Marcus, Mar 01 2021

cp's OEIS Frontend

A342036 Palindromes of even length only using 0 or 1.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Python

Ruby

Formula

Extensions

A342040 Binary palindromes of odd length.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Python

Formula

A342130 Decimal numbers m such that the product of the binary string of m and the binary string of m in reverse contains the binary string of m as a substring.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI