A075311 a(1) = 1; for n > 1, a(n) is the smallest number m > a(n-1) such that the number of 1's in the binary expansion of m is not already in the sequence.

1, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58, 60, 65, 66, 68, 71, 72, 75, 77, 78, 80, 83, 85, 86, 89, 90, 92, 96, 99, 101, 102, 105, 106, 108, 113, 114, 116, 120, 127, 129, 130, 132, 135, 136, 139, 141

Offset: 1

Author

Phil Carmody, Oct 11 2002

Keywords

• easy
• nonn

Comments

If A000120(k) is in the sequence then k is not.

Differs from A001969: 63 is not included since it has 6 bits set.

Examples

			We start with a(1)=1. Then 2 is not included since it has one bit set and 1 is in the sequence. Next, 3 is included since it has 2 one bits and 2 is not in the sequence. And so on.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Phil Carmody, Re: New sieve and a challenge
• Jon Perry, New sieve and a challenge
• Jon Perry and Phil Carmody, New sieve and a challenge, digest of 4 messages in primenumbers Yahoo group, Oct 11, 2002.

Crossrefs

Cf. A000120, A001969.

Cf. A075517, A217122.

Programs

Haskell

a075311 n = a075311_list !! (n-1)
a075311_list = 1 : f 2 [1] where
   f x ys = if a000120 x `elem` ys then f (x + 1) ys
                                   else x : f (x + 1) (x : ys)
-- Reinhard Zumkeller, Apr 22 2012

PARI

v=vector(1000): v[1]=1: for(curr=2,1000,e=A000120(curr): if(v[e],continue,v[curr]=1)): for(k=1,1000,if(v[k],print1(k",")))

Extensions

Edited by Ralf Stephan, Sep 14 2003