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A252867 a(n) = n if n <= 2, otherwise the smallest number not occurring earlier having in its binary representation at least one bit in common with a(n-2), but none with a(n-1). 10
0, 1, 2, 5, 10, 4, 3, 12, 17, 6, 9, 18, 8, 7, 24, 33, 14, 32, 11, 36, 19, 40, 16, 13, 48, 15, 80, 34, 20, 35, 28, 65, 22, 41, 66, 21, 42, 68, 25, 38, 72, 23, 64, 26, 69, 50, 73, 52, 67, 44, 81, 46, 129, 30, 97, 130, 29, 98, 132, 27, 100, 131, 56, 70, 49, 74, 37, 82 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Conjectured to be a permutation of the nonnegative integers. [Comment modified by N. J. A. Sloane, Jan 10 2015]

This is a purely set-based version of A098550, using the binary representation of numbers.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669, 2015.

EXAMPLE

The sequence of sets is {}, {0}, {1}, {0,2}, {1,3}, {2}, {0,1}, {3,4}. After the initial 3 terms, a(n) is the minimum set (as ordered by A048793) that has a nonempty intersection with a(n-2) but empty intersection with a(n-1).

Comment from N. J. A. Sloane, Dec 31 2014: The binary expansions of the first few terms are:

0  = 000000

1  = 000001

2  = 000010

5  = 000101

10 = 001010

4  = 000100

3  = 000011

12 = 001100

17 = 010001

6  = 000110

9  = 001001

18 = 010010

8  = 001000

7  = 000111

24 = 011000

33 = 100001

14 = 001110

32 = 100000

11 = 001011

36 = 100100

19 = 010011

40 = 101000

...

PROG

(PARI) invecn(v, k, x)=for(i=1, k, if(v[i]==x, return(i))); 0

alist(n)=local(v=vector(n, i, i-1), x); for(k=4, n, x=3; while(invecn(v, k-1, x)||!bitand(v[k-2], x)||bitand(v[k-1], x), x++); v[k]=x); v

(Haskell)

import Data.Bits ((.&.)); import Data.List (delete)

a252867 n = a252867_list !! n

a252867_list = 0 : 1 : 2 : f 1 2 [3..] where

   f :: Int -> Int -> [Int] -> [Int]

   f u v ws = g ws where

     g (x:xs) = if x .&. u > 0 && x .&. v == 0

                   then x : f v x (delete x ws) else g xs

-- Reinhard Zumkeller, Dec 24 2014

(Python)

A252867_list, l1, l2, s, b = [0, 1, 2], 2, 1, 3, set()

for _ in range(10**2):

....i = s

....while True:

........if not (i in b or i & l1) and i & l2:

............A252867_list.append(i)

............l2, l1 = l1, i

............b.add(i)

............while s in b:

................b.remove(s)

................s += 1

............break

........i += 1 # Chai Wah Wu, Dec 27 2014

CROSSREFS

Cf. A098550, A252865, A048793, A252868.

Reading this sequence mod 2 gives A253050 and A253051.

Cf. A253581, A253582, A253589 (binary weight), A253603.

Sequence in context: A064365 A177356 A078322 * A194356 A227317 A224300

Adjacent sequences:  A252864 A252865 A252866 * A252868 A252869 A252870

KEYWORD

nonn,base

AUTHOR

Franklin T. Adams-Watters, Dec 23 2014

STATUS

approved

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Last modified May 26 18:43 EDT 2017. Contains 287129 sequences.