cp's OEIS Frontend

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

%I A072823 #38 Oct 30 2024 13:30:20
%S A072823 1,7,11,13,14,15,19,21,22,23,25,26,27,28,29,30,31,35,37,38,39,41,42,
%T A072823 43,44,45,46,47,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,67,69,70,
%U A072823 71,73,74,75,76,77,78,79,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,97
%N A072823 Numbers that are not the sum of two powers of 2.
%C A072823 1 and integers with three or more 1-bits in their binary expansion. - _Vladimir Baltic_, Jul 23 2002
%C A072823 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 x<k. - _Gary Detlefs_, Jun 02 2014
%H A072823 Reinhard Zumkeller, <a href="/A072823/b072823.txt">Table of n, a(n) for n = 1..10000</a>
%F A072823 A073267(a(n)) = 0. [_Reinhard Zumkeller_, Mar 07 2012]
%p A072823 f:= x -> convert(convert(x,base,2),`+`)>2:
%p A072823 {1} union select(f, {$2..1000}); # _Robert Israel_, Jun 08 2014
%t A072823 Join[{1}, Select[Range[100], DigitCount[#, 2, 1] >= 3&]] (* _Jean-François Alcover_, Mar 08 2019 *)
%o A072823 (Haskell)
%o A072823 a072823 n = a072823_list !! (n-1)
%o A072823 a072823_list = tail $ elemIndices 0 a073267_list
%o A072823 -- _Reinhard Zumkeller_, Mar 07 2012
%o A072823 (Python)
%o A072823 from math import comb
%o A072823 from itertools import count, islice
%o A072823 def A072823(n):
%o A072823     def f(x):
%o A072823         s = bin(x)[2:]
%o A072823         c = n-1+(l:=len(s))+comb(l-1,2)
%o A072823         try:
%o A072823             c += l-1-s[1:].index('1')
%o A072823         except:
%o A072823             pass
%o A072823         return c
%o A072823     m, k = n-1, f(n-1)
%o A072823     while m != k: m, k = k, f(k)
%o A072823     return m
%o A072823 def A072823_gen(): # generator of terms
%o A072823     return filter(lambda n:n==1 or n.bit_count()>2,count(1))
%o A072823 A072823_list = list(islice(A072823_gen(),50)) # _Chai Wah Wu_, Oct 30 2024
%Y A072823 Cf. A000079, A048645, A073267.
%K A072823 nonn
%O A072823 1,2
%A A072823 _Jeremy Gardiner_, Jul 21 2002