A072823 Numbers that are not the sum of two powers of 2.

1, 7, 11, 13, 14, 15, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 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, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97

Offset: 1

Author

Jeremy Gardiner, Jul 21 2002

Keywords

• nonn

Comments

1 and integers with three or more 1-bits in their binary expansion. - Vladimir Baltic, Jul 23 2002

Appears to be the numbers k >1 for which there exist an x and y (x>y) such that x OR y = k, x+y != k, and xGary Detlefs, Jun 02 2014

Links

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

Crossrefs

Cf. A000079, A048645, A073267.

Programs

Haskell

a072823 n = a072823_list !! (n-1)
a072823_list = tail $ elemIndices 0 a073267_list
-- Reinhard Zumkeller, Mar 07 2012

Maple

f:= x -> convert(convert(x,base,2),`+`)>2:
{1} union select(f, {$2..1000}); # Robert Israel, Jun 08 2014

Mathematica

Join[{1}, Select[Range[100], DigitCount[#, 2, 1] >= 3&]] (* Jean-François Alcover, Mar 08 2019 *)

Python

from math import comb
from itertools import count, islice
def A072823(n):
    def f(x):
        s = bin(x)[2:]
        c = n-1+(l:=len(s))+comb(l-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 A072823_gen(): # generator of terms
    return filter(lambda n:n==1 or n.bit_count()>2,count(1))
A072823_list = list(islice(A072823_gen(),50)) # Chai Wah Wu, Oct 30 2024

Formula

A073267(a(n)) = 0. [Reinhard Zumkeller, Mar 07 2012]