A161989 Numbers having more than 2 or fewer than 2 ones in their binary representation.

0, 1, 2, 4, 7, 8, 11, 13, 14, 15, 16, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90

Offset: 1

Author

Reinhard Zumkeller, Jun 24 2009

Keywords

• nonn

Comments

A000120(a(n)) <> 2.

Complement of A018900; A151774(a(n)) = 0.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A018900, A151774.

Programs

Mathematica

Select[Range[0,100],DigitCount[#,2,1]!=2&] (* Harvey P. Dale, Mar 11 2013 *)

PARI

isok(n) = hammingweight(n) != 2; \\ Michel Marcus, Nov 01 2019

Python

from itertools import count, islice
from math import comb
def A161989(n):
    def f(x):
        s = bin(x)[2:]
        c = n-1+comb((l:=len(s))-1,2)
        try:
            c += l-1-s[1:].index('1')
        except:
            pass
        return c
    m, k = n-1, f(n-1)
    while m != k: m, k = k, f(k)
    return m
def A161989_gen(): # generator of terms
    return filter(lambda n:n.bit_count()!=2,count(0))
A161989_list = list(islice(A161989_gen(),50)) # Chai Wah Wu, Oct 30 2024