A226077 a(1)=1; a(n) = smallest positive integer not yet in the sequence, such that a(n) and a(n-1) have exactly one common 1-bit in their binary representations.

1, 3, 2, 6, 4, 5, 9, 7, 10, 8, 11, 12, 20, 13, 17, 15, 18, 14, 19, 16, 21, 24, 22, 25, 33, 23, 34, 26, 35, 29, 36, 28, 37, 27, 38, 32, 39, 40, 30, 41, 48, 31, 65, 43, 52, 42, 49, 44, 50, 45, 67, 46, 66, 47, 68, 53, 70, 51, 69, 54, 74, 55, 73, 56, 72, 57, 71, 58, 76, 59, 80, 60, 75, 64, 77, 82, 61, 96, 62, 81, 78, 97, 84, 98, 85, 104, 83, 100, 88

Offset: 1

Author

Paul Tek, May 25 2013

Keywords

• nonn
• base

Comments

A000120(a(n) & a(n+1))=1, where & stands for the bitwise AND operator.

Permutation of the natural numbers with inverse A226093. - Reinhard Zumkeller, May 26 2013

Examples

			a(1)=1 by definition.
A000120(a(1) & 2)=0, A000120(a(1) & 3)=1, hence a(2)=3.
A000120(a(2) & 2)=1, hence a(3)=2.
A000120(a(3) & 4)=0, A000120(a(3) & 5)=0, A000120(a(3) & 6)=1, hence a(4)=6.
A000120(a(4) & 4)=1, hence a(5)=4.
A000120(a(5) & 5)=1, hence a(6)=5.
A000120(a(6) & 7)=2, A000120(a(6) & 8)=0, A000120(a(6) & 9)=1, hence a(7)=9.
A000120(a(7) & 7)=1, hence a(8)=7.
A000120(a(8) & 8)=0, A000120(a(8) & 10)=1, hence a(9)=10.
A000120(a(9) & 8)=1, hence a(10)=8.
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A109812, A115510, A000120.

Cf. A209229.

Programs

Haskell

import Data.Bits ((.&.))
import Data.List (delete)
a226077 n = a226077_list !! (n-1)
a226077_list = 1 : f 1 [2..] where
   f :: Integer -> [Integer] -> [Integer]
   f x zs = g zs where
     g (y:ys) | a209229 (x .&. y) == 0 = g ys
              | otherwise = y : f y (delete y zs)
-- Reinhard Zumkeller, May 26 2013