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

1,2

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.

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.

Example

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.

Prog

(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", ")))
(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

Crossrefs

Cf. A000120, A001969.

Cf. A075517, A217122.

Sequence in context: A241571 A080307 A001969 * A032786 A080309 A281746

Adjacent sequences: A075308 A075309 A075310 * A075312 A075313 A075314

Keyword

easy,nonn

Author

Phil Carmody, Oct 11 2002

Extensions

Edited by Ralf Stephan, Sep 14 2003

Status

approved