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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.

%I A374990 #12 Jul 28 2024 12:50:35
%S A374990 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,
%T A374990 43,27,39,46,47,31,65,16,81,24,73,20,25,28,69,18,85,26,77,45,29,30,67,
%U A374990 70,83,51,75,86,91,59,71,78,87,55,79,94,95,63,129,32,161
%N 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.
%C A374990 Leading zeros in binary expansions are ignored.
%C A374990 This sequence is a self-inverse permutation of the nonnegative integers.
%H A374990 Rémy Sigrist, <a href="/A374990/b374990.txt">Table of n, a(n) for n = 0..8191</a>
%H A374990 Rémy Sigrist, <a href="/A374990/a374990.gp.txt">PARI program</a>
%H A374990 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A374990 The first terms, in decimal and in binary, alongside an appropriate palindrome, are:
%e A374990   n   a(n)  bin(n)  bin(a(n))  palindromes
%e A374990   --  ----  ------  ---------  -----------
%e A374990    0     0       0          0            0
%e A374990    1     1       1          1           11
%e A374990    2     5      10        101        10101
%e A374990    3     3      11         11         1111
%e A374990    4     9     100       1001      1001001
%e A374990    5     2     101         10        10101
%e A374990    6    11     110       1011      1101011
%e A374990    7     7     111        111       111111
%e A374990    8    17    1000      10001    100010001
%e A374990    9     4    1001        100      1001001
%e A374990   10    21    1010      10101    101010101
%e A374990   11     6    1011        110      1101011
%e A374990   12    19    1100      10011    110010011
%o A374990 (PARI) \\ See Links section.
%o A374990 (Python)
%o A374990 from itertools import count, islice
%o A374990 def p(s): return s == s[::-1]
%o A374990 def c(v, w): return p(v+w) or p(w+v)
%o A374990 def agen(): # generator of terms
%o A374990     mink, a = 0, set()
%o A374990     for n in count(0):
%o A374990         bn = bin(n)[2:]
%o A374990         an = next(k for k in count(mink) if k not in a and c(bin(k)[2:], bn))
%o A374990         yield an
%o A374990         a.add(an)
%o A374990         while mink in a: mink += 1
%o A374990 print(list(islice(agen(), 70))) # _Michael S. Branicky_, Jul 28 2024
%Y A374990 Cf. A006995, A057889.
%K A374990 nonn,base
%O A374990 0,3
%A A374990 _Rémy Sigrist_, Jul 26 2024