|
%I #28 Oct 17 2022 08:38:14
%S 0,2,3,5,7,8,9,10,11,12,14,16,17,19,20,22,24,25,26,27,28,29,31,33,34,
%T 35,36,38,40,41,42,43,44,45,47,49,50,52,53,55,57,58,59,60,61,62,64,65,
%U 66,67,68,69,70,72,73,74,75,76,77,79,81,82,84,85,87,89,90
%N Numbers that are of the form k + sum of binary digits of k for some nonnegative integer k.
%C Complement of A010061.
%C Obtained when A092391 is sorted and duplicates are removed.
%C The asymptotic density of this sequence is 1 - (1/8) * (Sum_{n>=1} 1/2^a(n))^2 = 1 - A242403 = 0.747339... - _Amiram Eldar_, Nov 28 2020
%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.24, pp. 179-180.
%D József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384-386.
%D G. Troi and U. Zannier, Note on the density constant in the distribution of self-numbers, Bolletino U. M. I. (7) 9-A (1995), 143-148.
%H Antti Karttunen, <a href="/A228082/b228082.txt">Table of n, a(n) for n = 1..8192</a>
%H G. Troi and U. Zannier, <a href="http://dml.mathdoc.fr/item/BUMI_1999_8_2B_2_397_0/">Note on the density constant in the distribution of self-numbers. II</a>, Bollettino dell'Unione Matematica Italiana 2-A (1999), 397-399.
%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%t Table[n + Total[IntegerDigits[n, 2]], {n, 0, 100}] // Union (* _Jean-François Alcover_, Sep 03 2013 *)
%o (Haskell)
%o a228082 n = a228082_list !! (n-1)
%o a228082_list = 0 : filter ((> 0) . a228085) [1..]
%o -- _Reinhard Zumkeller_, Oct 13 2013
%Y Numbers that occur to the right of the leftmost column of A228083. Positions of nonzeros in A228085. A superset of A228088.
%Y Cf. also A227643, A005187, A230091, A230092, A227915, A242403.
%Y The even terms are the first row of A350601.
%K nonn,base
%O 1,2
%A _Antti Karttunen_, Aug 09 2013
|
