A374990 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the concatenation of the binary expansions of n and a(n), in at least one way, is palindromic.

0, 1, 5, 3, 9, 2, 11, 7, 17, 4, 21, 6, 19, 22, 23, 15, 33, 8, 41, 12, 37, 10, 13, 14, 35, 38, 43, 27, 39, 46, 47, 31, 65, 16, 81, 24, 73, 20, 25, 28, 69, 18, 85, 26, 77, 45, 29, 30, 67, 70, 83, 51, 75, 86, 91, 59, 71, 78, 87, 55, 79, 94, 95, 63, 129, 32, 161

Offset

0,3

Comments

Leading zeros in binary expansions are ignored.

This sequence is a self-inverse permutation of the nonnegative integers.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, in decimal and in binary, alongside an appropriate palindrome, are:
  n   a(n)  bin(n)  bin(a(n))  palindromes
  --  ----  ------  ---------  -----------
   0     0       0          0            0
   1     1       1          1           11
   2     5      10        101        10101
   3     3      11         11         1111
   4     9     100       1001      1001001
   5     2     101         10        10101
   6    11     110       1011      1101011
   7     7     111        111       111111
   8    17    1000      10001    100010001
   9     4    1001        100      1001001
  10    21    1010      10101    101010101
  11     6    1011        110      1101011
  12    19    1100      10011    110010011

Prog

(PARI) \\ See Links section.
(Python)
from itertools import count, islice
def p(s): return s == s[::-1]
def c(v, w): return p(v+w) or p(w+v)
def agen(): # generator of terms
    mink, a = 0, set()
    for n in count(0):
        bn = bin(n)[2:]
        an = next(k for k in count(mink) if k not in a and c(bin(k)[2:], bn))
        yield an
        a.add(an)
        while mink in a: mink += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Jul 28 2024

Crossrefs

Cf. A006995, A057889.

Sequence in context: A112812 A241624 A159275 * A059031 A245516 A073243

Adjacent sequences: A374987 A374988 A374989 * A374991 A374992 A374993

Keyword

nonn,base

Author

Rémy Sigrist, Jul 26 2024

Status

approved