number.wiki

Term

Binary Palindrome

Numbers whose binary representation reads the same forwards and backwards (5 = 101, 7 = 111, 9 = 1001, 21 = 10101).

154 numbers tagged.

A binary palindrome has a base-2 representation that reads identically in both directions: 5 is 101, 7 is 111, 9 is 1001, 21 is 10101, 27 is 11011.

Palindromicity is base-dependent — a number can be a palindrome in binary without being one in decimal, and vice versa. Binary palindromes thin out roughly like √n (there are about 2√n of them below n), so they're uncommon enough to be a distinctive property.

The decimal palindromes have their own [[palindrome]] tag; a page may also note which other bases (2–16) it reads palindromically in.

The sequence of binary palindromes is OEIS A006995.

5 7 9 15 17 21 27 31 33 45 51 63 65 73 85 93 99 107 119 127 129 153 165 189 195 219 231 255 257 273 297 313 325 341 365 381 387 403 427 443 455 471 495 511 513 561 585 633 645 693 717 765 771 819 843 891 903 951 975 1,023 1,025 1,057 1,105 1,137 1,161 1,193 1,241 1,273 1,285 1,317 1,365 1,397 1,421 1,453 1,501 1,533 1,539 1,571 1,619 1,651 1,675 1,707 1,755 1,787 1,799 1,831 1,879 1,911 1,935 1,967 2,015 2,047 2,049 4,889 5,113 5,189 5,557 5,869 5,981 6,211 6,827 7,607 7,759 7,919 8,191 17,377 18,097 18,289 19,433 19,609 19,801 21,157 22,541 22,669 22,861 23,581 24,029 25,747 25,939 27,179 27,803 28,123 28,219 28,807 29,671 30,391 31,183 31,727 65,535 65,537 70,289 71,633 72,817 74,377 75,721 77,801 77,849 79,193 81,017 83,269 83,653 85,093 85,733 86,293 86,677 88,117 92,461 95,581 96,221 97,213 98,563 98,947 2,147,483,647 4,294,967,295