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

1,3

Comments

A000120(a(n)) <> 2.

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

Links

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000120, A018900, A151774.

Sequence in context: A307284 A323108 A187418 * A229829 A000069 A344602

Adjacent sequences: A161986 A161987 A161988 * A161990 A161991 A161992

Keyword

nonn

Author

Reinhard Zumkeller, Jun 24 2009

Status

approved