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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.
2
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.
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
Sequence in context: A112812 A241624 A159275 * A059031 A245516 A073243
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jul 26 2024
STATUS
approved