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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A230892 Terms of A230891 written in base 10: the binary expansions of a(n) and a(n+1) taken together can be rearranged to form a palindrome.

Original entry on oeis.org

0, 3, 1, 2, 4, 7, 8, 5, 6, 9, 10, 12, 15, 16, 11, 13, 14, 17, 18, 20, 23, 24, 27, 29, 30, 32, 19, 21, 22, 25, 26, 28, 31, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58, 60, 63, 64, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62, 65, 66, 68, 71
Offset: 0

Views

Author

N. J. A. Sloane, Nov 11 2013

Keywords

Comments

See A230891 for precise definition.
Just as for A228407, we can ask: does every number appear? The answer is yes - see the Comments in A228407.
The difference d(n)=a(n)-n increases from d(3*2^(k-2)+2) = 1-2^(k-2) to d(3*2^(k-1)+1) = 1-2^(k-1), going through 0 at n=2^k+1 and n=2^k+2, cf. examples. - M. F. Hasler, Nov 12 2013
From Robert G. Wilson v, Nov 15 2013: (Start)
Beginning with k=3, each "grouping" of ever increasing terms, begins at 2^k + 3 and runs up to 2^(k+2) and includes 3*2^(k-1) terms.
Indices of powers of 2 occur at: 2, 3, 4, 6, 13, 25, 49, 97, 193, 385, 769, 1537, ..., which, except for 2, 3 & 6, is A181565: 3*2^n + 1.
When the index equals the term: 0, 4, 9, 10, 17, 18, 33, 34, 65, 66, 129, 130, 257, 258, 513, 514, 1025, 1026, 2049, 2050, ..., .
Parity of a(n) beginning at n=0: 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, ..., . (End)

Examples

			From _M. F. Hasler_, Nov 12 2013: (Start)
Let d(n)=a(n)-n, i.e., a(n)=n+d(n). Then we have, after initial values d(0..8)=(0, 2, -1, -1, 0, 2, 2, -2, -2), the
following pattern: d(9) = d(10) = 0, ..., d(13) = 3,
d(14) = -3, ..., d(17) = d(18) = 0, ..., d(25) = 7;
d(26) = -7, ..., d(33) = d(34) = 0, ..., d(49) = 15,
d(50) = -15, ..., d(65) = d(66) = 0, ..., d(97) = 31,
d(98) = -31, ..., d(129) = d(130) = 0, ..., d(193) = 63,
d(194) = -63,..., d(257) = d(258) = 0, ... (End)
		

Crossrefs

Programs

  • PARI
    {u=0; a=0; La=1; ha=0/*hack*/; for(n=1, 99, u+=1<=2^L,L++); bittest(ha+h=hammingweight(k),0)&&!bittest(La+L,0)&&next; !a&&k<3&&next; a=k; ha=h; La=L; break))} \\ M. F. Hasler, Nov 11 2013
    
  • Python
    from collections import Counter
    A230892_list, l, s, b = [0, 3], Counter('11'), 1, {3}
    for _ in range(30001):
        i = s
        while True:
            if i not in b:
                li, o = Counter(bin(i)[2:]), 0
                for d in (l+li).values():
                    if d % 2:
                        if o > 0:
                            break
                        o += 1
                else:
                    A230892_list.append(i)
                    l = li
                    b.add(i)
                    while s in b:
                        b.remove(s)
                        s += 1
                    break
            i += 1 # Chai Wah Wu, Jun 19 2016