A094510 -id:A094510 - cp's OEIS frontend

A094511 Smallest number distinct from n, not occurring earlier and having in binary representation not more ones than n.

2, 1, 4, 8, 3, 5, 6, 16, 10, 9, 7, 17, 11, 12, 13, 32, 18, 20, 14, 24, 19, 21, 15, 33, 22, 25, 23, 26, 27, 28, 29, 64, 34, 36, 37, 40, 35, 41, 30, 48, 38, 44, 39, 42, 43, 45, 31, 65, 50, 49, 46, 56, 51, 52, 47, 66, 53, 54, 55, 57, 58, 59, 60, 128, 68, 72, 69, 80, 67, 73, 70

Offset: 1

Reinhard Zumkeller, May 06 2004

nonn

Permutation of the natural numbers: A094512(a(n))=a(A094512(n))=n.

Cf. A007088, A000120, A094513, A094510.

import Data.List (delete)
a094511 n = a094511_list !! (n-1)
a094511_list = f 1 [1..] where
   f x zs = g zs where
     g (y:ys) = if y /= x && a000120 y <= wt
                   then y : f (x + 1) (delete y zs) else g ys
     wt = a000120 x
-- Reinhard Zumkeller, Nov 23 2014

A112411 a(n) = smallest positive integer, not occurring earlier in the sequence and not equal to n, that has the same number of (non-leading) 0's in its binary representation as n.

Original entry on oeis.org

3, 5, 1, 9, 2, 11, 15, 17, 4, 12, 6, 10, 14, 13, 7, 33, 8, 20, 21, 18, 19, 25, 27, 35, 22, 28, 23, 26, 30, 29, 63, 65, 16, 36, 24, 34, 38, 37, 43, 48, 42, 41, 39, 49, 46, 45, 55, 40, 44, 52, 53, 50, 51, 57, 47, 71, 54, 60, 61, 58, 59, 95, 31, 129, 32, 68, 69, 66, 67, 73, 56, 80

Offset: 1

Leroy Quet, Dec 08 2005

Sequence is a permutation of the positive integers. It is its own inverse permutation.

			Among positive integers not among the first 8 terms of the sequence, 4 (100 in binary) is the smallest positive integer which has the same number of non-leading zeros in its binary representation as 9 (1001 in binary). So a(9) = 4.

Cf. A007814, A023416, A140977, A094510.

from itertools import islice
def val(n): return (~n & n-1).bit_length() # From Chai Wah Wu in A007814
def next0(n):
    z = val(n)
    f = (n|(2**z)-1) + 1
    w = val(f)
    if f != 2**w: z+=1
    return(f|(2**(w-z)-1))
def a_gen():
    B,n = [],1
    while True:
        f = 0
        for i in B:
            if i[0] == n:
                f+=1; n+=1; yield(i[1]); B.remove(i); break
        if f < 1:
            B.append((next0(n),n)); yield(next0(n)); n+=1
A112411_list = list(islice(a_gen(), 100)) # John Tyler Rascoe, Mar 20 2024

More terms from R. J. Mathar, Feb 08 2008

cp's OEIS Frontend

A094511 Smallest number distinct from n, not occurring earlier and having in binary representation not more ones than n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell