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

1,2

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

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Example

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.

Prog

(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

Crossrefs

Cf. A109812, A115510, A000120.

Cf. A209229.

Sequence in context: A303775 A084494 A084498 * A352200 A066182 A195114

Adjacent sequences: A226074 A226075 A226076 * A226078 A226079 A226080

Keyword

nonn,base

Author

Paul Tek, May 25 2013

Status

approved